A polynomial of degree 4 will have 4 zeros. The zero of 3 with a multiplicity of 2 counts as two of these zeros. You've also been given a zero of -i. So it seems that we only have 3 of the 4 zeros. We need all 4 to be able to form the desired polynomial.
You didn't mention that the polynomial should have real coefficients. But I'm going to assume it because otherwise we can't solve the problem. If a polynomial with real coefficients has a complex zero, then the complex conjugate of that complex zero will also be a zero. This is how we will find the 4th zero.
A complex number in standard form is a + bi. Its complex conjugate is a + (-bi) or a - bi. The complex zero we were given is -i. In standard form this would be 0 + (-i). The complex conjugate of 0 + (-i) would be 0 - (-i) or 0 + i or just i.
So the four zeros of the desired polynomial are 3 (twice), -i and i. If a number "z" is a zero of a polynomial then (x - z) is a factor of that polynomial. Using this fact and the four zeros we can write a factored form of our desired polynomial:
f%28x%29+=+a%28x-3%29%28x-3%29%28x-%28-i%29%29%28x-i%29
Simplifying the 3rd factor we get:
f%28x%29+=+a%28x-3%29%28x-3%29%28x%2Bi%29%28x-i%29
where the "a" is any non-zero number. Since there are an infinite number of non-zero numbers, there will be an infinite number of possible correct solutions to this problem. To make things easy we will choose to make "a" be 1. This makes our factored polynomial:
f%28x%29+=+%28x-3%29%28x-3%29%28x%2Bi%29%28x-i%29
All we have to do now is multiply this out. We can simplify this process if we take advantage of some factoring patterns. The first two factors can be multiplied using:
%28a-b%29%5E2+=+a%5E2-2ab%2Bb%5E2
And the last two factors can be multiplied using:
%28a%2Bb%29%28a-b%29+=+a%5E2-b%5E2
With these patterns we get:
f%28x%29+=+%28%28x%29%5E2-2%28x%29%283%29%2B%283%29%5E2%29%28%28x%29%5E2-%28i%29%5E2%29
Simplifying inside each factor we get:
f%28x%29+=+%28x%5E2-6x%2B9%29%28x%5E2-i%5E2%29
And since i%5E2+=+-1 this becomes:
f%28x%29+=+%28x%5E2-6x%2B9%29%28x%5E2-%28-1%29%29
or
f%28x%29+=+%28x%5E2-6x%2B9%29%28x%5E2%2B1%29
We have one more multiplication. There are no shortcuts for this one. We have to multiply each term of one factor times each term of the other and then add like terms, if any:
f%28x%29+=+x%5E2%2Ax%5E2%2Bx%5E2%2A1%2B%28-6x%29%2Ax%5E2%2B%28-6x%29%2A1%2B9%2Ax%5E2%2B9%2A1
Simplifying...
f%28x%29+=+x%5E4%2Bx%5E2%2B%28-6x%5E3%29%2B%28-6x%29%2B9x%5E2%2B9
f%28x%29+=+x%5E4%2B10x%5E2%2B%28-6x%5E3%29%2B%28-6x%29%2B9
Re-ordering into standard form:
f%28x%29+=+x%5E4%2B%28-6x%5E3%29%2B10x%5E2%2B%28-6x%29%2B9
This is a polynomial function of degree 4 with the given zeros.
P.S. As mentioned earlier, this is not the only possible correct answer. This is the answer when you make "a" equal to 1. Other values for "a" give us different polynomial functions which also have the same zeros. For example, if we had chosen a = 2 we would have gotten f%28x%29+=+2x%5E4%2B%28-12x%5E3%29%2B20x%5E2%2B%28-12x%29%2B18.
The table below represents which equation?
х
0
2.
-1
1
1
-5
2
-8
у
-2
A
y = -x
B
y = 3x + 6
y=-3x - 2
D
y = x + 2
Answer:
C: y = -3x - 2
Step-by-step explanation:
See attached image. Use a spreasheet to calculate the values of y for each vale of x and compare the results. Equation C matches the data in the table.
-1.6, 5/2, -7/8, 0.9, -6/5 from least to greatest
Answer:
starting with least...
-1.6
-6/5
-7/8
9/10
5/2
...to greatest.
Step-by-step explanation:
start by putting the decimals into fractions:
-1.6 = -8/5
0.9 = 9/10
and then find a common denominator to compare them fairly.
the number that they all end up going into is 40, which will be your common demoninator.
-8/5 (aka -1.6) = -64/40
5/2 = 100/40
-7/8 = -35/40
9/10 (aka 0.9) = 36/40
-6/5 = -48/40
Enter the correct answer in the box. Simplify the expression (6^4)^2.
Answer:
1679616
Step-by-step explanation:
(6^4) = 1296
1296^2 = 1679616
Martha can paint a room in 2 hours. Jamie can paint the same room in 6 hours. How long, to the nearest 10th of an hour, will it take them to paint the room together?
Answer:
0.6 hours or 40 mins
Step-by-step explanation:
1/2 + 1/6 = 2/3
Solve the following....
[tex]2(x-3)=2x+4[/tex]
Answer:
No answer. The question is not correct. 2x-6 cannot be equal to 2x+4
Step-by-step explanation:
2(x-3) = 2x+4
2x-6 = 2x+4
This can't be true. 2x-6 cannot be equal to 2x+4:
Subtract 2x from both sides and we are left with -6 = 4: FALSE
Answer:
no solutionStep-by-step explanation:
Taking the LHS and distributing
2(x - 3)2(x) - 2(3)2x - 6Equating to the RHS
2x - 6 = 2x + 4On inputting any value for x, this equation will not be correct.
Hence, it has no solution.
what are the two correct answers?
Answer:
y ≥ 1 or y ≤ -2.4
Explanation:
| 10y + 7 | ≥ 17
---------------------
[tex]\sf {Apply\:absolute\:rule}:\quad \mathrm{If}\:|u|\:\ge \:a,\:a\: > \:0\:\mathrm{then}\:u\:\le \:-a\:\quad \mathrm{or}\quad \:u\:\ge \:a[/tex]
-------------------------
10y + 7 ≤ -1710y ≤ -17 - 710y ≤ -24y ≤ -2.4-------------------------
10y + 7 ≥ 1710y ≥ 10y ≥ 1I think my brain is messed up right now please help me with this
Answer:
5 million.
Step-by-step explanation:
1 hundred thousand = 100,000
50 of these = 5,000,000 (replacing the 1 in 100,000 by 50)
and this = 5 million.
Find the equation of the quadratic function with vertex (– 2, – 6) that goes through the point (-4, -18)
Answer:
y = -3(x+2)^2 - 6
Step-by-step explanation:
y = a(x+2)^2 -6
-18 = a(-2)^2 - 6
-12 = 4a
a = -3
y = -3(x+2)^2 - 6
A student chosen at random from a class of 12 girls and 14 boys. What is the probability that the student chosen is not a girl ?
help nowwww
These polygons are similar.
What is the value of x?
• A. 16
20.25
O c 21
•
24.75
• E 36
Answer:
20
Step-by-step explanation:
As they are similar, correspondence sides are in common ratios:
Apply cross product property
Multiply the numbers
Divide both sides of the equation by 5
Calculate
A , B , C , D ??????????????????????
Answer:
3 2/3 cups
Step-by-step explanation:
1 1/3 for one recipe.
2/3 cups for the second recipe.
1 2/3 for the third recipe.
Add all of the amount of cups used to get the total amount of sugar used.
1 1/3 + 2/3 + 1 2/3 = 3 2/3
She used 3 2/3 cups of sugar in all.
hope this helps!! p.s. i really need brainliest :)
Given circle E with diameter CD and radius EA. AB is tangent to E at A. if AD = 15 and EC = 14, solve for AC.
Answer:
AC ≈ 23.6 units
Step-by-step explanation:
m∠CAD = 90°
CD = 2×14 = 28 , AD = 15
CD² = AD² + AC² ⇒ AC² = CD² - AD²
AC² = 28² - 15² = ( 28 - 15 )( 28 + 15 ) = 13 × 43 = 559
AC ≈ 23.6
Help me quickly please, im not good at this kind of math.
Answer:
*Bottom*
Step-by-step explanation:
so hat is $8.50
gloves are $51
cleats are $85
cleats are $76.50 more than the hat.
in which age bracket does the most number of parcitipants fall?
The most number of participants fall on the age bracket of 37-39.
hope this helps
Help me pls very pls
Answer:
y = 4
Step-by-Step explanation:
4x5 = 20
2x5 = 10
20+10=30.
(4x5) + (2x5) = 30
or
(yx5) + (2x5) = 30
Brainliest would be appriciated :) have a nice day!
Alejandro will deposit $1,750 in an account that earns 6.5% simple interest every year. His sister Anallency will deposit $1,675 in an account that earns 7.5% interest compounded annually. The deposits will be made on the same day, and no additional money will be deposited or withdrawn from the accounts. Which sibling will have more money at the end of four years?
Answer: Anallency
Step-by-step explanation:
First, lets make two equations for both siblings, using the base: SI = P(1 + rt) and CI = P(1 + r/n)^nt
Alejandro = 1750(1 + 0.065[4]) = 1750 + 455 = $2,205
Anallency = 1675(1 + 0.075/1)^4 = $2236.91
After 4 years, Alejandro will have $2,205, and Anallency will have $2236.91
Since $2236.91 > 2,205, Anallency will have more money after 4 years.
Answer:
Anallency will have mor money.
Step-by-step explanation:
Simple Interest:
I = Prt
I = $1750 × 0.065 × 4
I = $455
Total after 4 years: $1750 + $455 = $2205
Compound Interest:
F = P(1 + r/n)^(nt)
F = $1675(1 + 0.075)^(4)
F = $2236.91
Answer: Anallency will have mor money.
Which expression represents "eight less
than twice a number"?
Answer:
2n-8
Step-by-step explanation:
The expression eight less then twice a number will be shown in the following steps.
First, we tackle the first part of the sentence “Eight less” from here we can derive that there is a -8 in the expression.
Secondly, we can tackle the second part “twice a number” so this would be mean 2 times N, or 2n
From the two steps previously we can the conclude the answer must be 2n-8
A manager drew this box-and-whisker plot to represent the weights, in pounds, of the 440 crates the company is shipping.
Box-and-whisker plot ranging from 80 to 180 with ticks at increments of 2.5. Plot defined by points at 84, 99.5, 113, 143, 170.
How many crates weigh more than 99.5 pounds?
Select from the drop-down menu to correctly complete the statement.
About
Choose...
crates weigh more than 99.5 pounds.
Answer:
330
Step-by-step explanation:
took the test
Answer:
330 is the answer.
Step-by-step explanation:
is the theoretical or the experimental probability greater for the coin landing on tails?
what is 2+2+9+0+8+1+2+3+4+5+6+7+8+9
Answer:
66
Step-by-step explanation:
adding all shown numbers without a calculator = 66
select the correct location on the number line which point on the number line represents the approximate volume of a cylinder with a radius of 4 units snd a height of 4 units?
Answer:
Step-by-step explanation:
Volume = Volume = π r^2 h r^2 h
= 4^2 * 4 * π
= 64π
which is about 64 * 22/7
= 200
which is the 5th point from the left.
Find the length of h. Round to the nearest hundreth.
Answer:
h = 0.24
Step-by-step explanation:
Assuming this is a parallelogram...
Sine trig ratio
[tex]\sin(\theta)=\sf \dfrac{O}{H}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleH is the hypotenuseLet x be the angle in the top left of the parallelogram.
[tex]\implies \sin(x)=\dfrac{0.3}{0.5}=\dfrac35[/tex]
Opposite angles in a parallelogram are congruent.
Therefore, the angle in the bottom right of the parallelogram is also x.
[tex]\implies \sin(x)=\dfrac{h}{0.4}[/tex]
[tex]\textsf{As} \:\sin(x)=\dfrac35[/tex]
[tex]\implies \dfrac35=\dfrac{h}{0.4}[/tex]
[tex]\implies h=\dfrac35 \cdot 0.4=0.24[/tex]
Remember (3,4,5) Pythagorean triplet
Triangle containing y
Hypotenuse=0.5Base=0.4Triangle containing x
Base=0.4Perpendicular=0.3Now use ratio to find
0.5/0.3=0.4/h5/3=0.4/h5h=1.2h=1.2/5h=0.24GIVING BRAINLEST TO THE PERSON THAT CAN EXPLAIN HOW TO DO THIS THE BEST :)
Answer:
196 - 49[tex]\pi[/tex]
i hope this helped :)
Step-by-step explanation:
first of all the explaination is to first find the area of the square and then the circle after you have found that you should subtract them and you will get the area of the shaded region.
radius x 2 = the side of the square
7 x 2 = 14
area of square - 14 x 14 = 196 squared
formula of finding the area of the circle - [tex]\pi[/tex]r^2
area of circle - 3.14 x 7 x 7 = 49[tex]\pi[/tex]
so answer simpliefied is 196 - 49[tex]\pi[/tex]
i hope this helped
If the average annual interest rate is 17.11%, how many months will it take the average American family to pay off their debt of $7,942 if they make a minimum payment of $175 each month and no additional purchases are made? months.
The payoff period will be 73.56 months if the average annual interest rate is 17.11%, how many months will it take the average American family to pay off their debt of $7,942
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
We have:
Loan amount = $7942, Monthy pay = $175, Interest rate = 17.11%
After calculating from the payment formula:
The payoff = 6.13 years = 73.56 months
Thus, the payoff period will be 73.56 months if the average annual interest rate is 17.11%, how many months will it take the average American family to pay off their debt of $7,942
Learn more about the compound interest here:
brainly.com/question/26457073
#SPJ1
if 1 foot equals 20 feet, 151 feet = ? (scale factor)
Answer:
3020
Step-by-step explanation:
Write the equation of the line that passes through the points (-3, -5) and
(-2,-4). Put your answer in fully simplified point-slope form, unless it is a vertical
or horizontal line.
What is the measure of ∠P ?
with explanation pls
Answer:
80°
Step-by-step explanation:
we know angle R and angle Q are equal cause of the dashes
so
2x+30=6x-10
and then solve
30=4x-10
40=4x
10°=x
since they're equal just plug in X for one
2(10)+30= angle r
50° = angle r
we have two 50° angles and we know every triangle is 180°
so create the formula
angle r + angle q + angle p =180°
fill it in
50° + 50° + p = 180°
so angle p= 80°
How does the graph of f(x) = (x − 1)2 relate to the basic function f(x) = x2?
Answer:
Shift 1 unit to the right
Step-by-step explanation:
Note: Both functions can not be represented by f(x) and square is missing in basic function.
The given basic function is
The given function is
So, the given function can be written in the form of basic form as
...(1)
The translation is defined as
.... (2)
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
On comparing (1) and (2), we get
Therefore, graph of f(x) shift 1 unit to the right to get graph of g(x).
Answer: b.) shift 1 unit to the right
Step-by-step explanation: on edg 2020
Hello, I was just doing some practicing for adding integers. I did some problems on my own and I was wondering if I am on the right track.
Answer:
Yes
Step-by-step explanation:
Is Okay.
but when the answer is a positive answer ignore the + sign
but if negative show it
apart from that it's all okay
Prove
[tex]\small \dfrac{ \sin(A) - \cos(A) + 1}{\sin(A) + \cos(A) - 1} = \dfrac{\cos(A)}{1 - \sin(A) } [/tex]
Help!!!!!!!!!
[tex] \frac{ \sin(a) - \cos(a) + 1 }{ \sin(a) + \cos(a) - 1 } = \\ [/tex]
____________________________________________
[tex] \frac{ \sin(a) - \cos(a) + 1 }{ \sin(a) + \cos(a) - 1 } \times \frac{ \sin(a) + \cos(a) + 1}{ \sin(a) + \cos(a) + 1 } = [/tex]
[tex] \frac{ {sin}^{2}(a) + 2 \sin(a) - {cos}^{2} (a) + 1 }{ {sin}^{2}(a) + 2 \sin(a) \cos(a) + {cos}^{2}(a) - 1 } = [/tex]
_____________________________________________
As you know :
[tex] {sin}^{2} (a) + {cos}^{2} (a) = 1[/tex]
_____________________________________________
[tex] \frac{ {sin}^{2} (a) - {cos}^{2}(a) + 2 \sin(a) + 1}{ {sin}^{2} (a) + {cos}^{2}(a) - 1 + 2 \sin(a) \cos(a) } = [/tex]
[tex] \frac{ {sin}^{2}(a) - (1 - {sin}^{2}(a)) + 2 \sin(a) + 1 }{1 - 1 + 2 \sin(a) \cos(a) } = [/tex]
[tex] \frac{ {sin}^{2} (a) + {sin}^{2} (a) - 1 + 1 + 2 \sin(a) }{2 \sin(a) \cos(a) } = [/tex]
[tex] \frac{2 {sin}^{2}(a) + 2 \sin(a) }{2 \sin(a) \cos(a) } = [/tex]
[tex] \frac{2 \sin(a)( \sin(a) + 1) }{2 \sin(a)( \cos(a) \: ) } = \\ [/tex]
[tex] \frac{ \sin(a) + 1}{ \cos(a) } \\ [/tex]
And we're done...
Take care ♡♡♡♡♡