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3 years ago

Which of the following is a polynomial with roots 5, 4i, and -4i?

Mathematics

1 answer:

solniwko [45]3 years ago

8 0

The correct answer is x^3 - 5x^2 + 16x - 80.

In order to find this, we work backwards. Start by creating true statements for each of the roots.

x = 5

x = +/-4i

Now we can solve all of these until they are statements that equal 0.

x = 5 ----> Subtract 5 from both sides

x - 5 = 0

x = +/-4i ------> Square both sides

x^2 = -16 ---> Add 16 to both sides.

x^2 + 16 = 0

Now we can use the two statements that we have and multiply them to get the polynomial.

(x - 5)(x^2 + 16)

x^3 - 5x^2 + 16x - 80

You might be interested in

Calculate the area of triangle ABC with altitude CD, given A(−7, −1), B(−1, 5), C(0, 0), and D(−3, 3)

Snezhnost [94]

Answer:

A=25 (Rounded)

Step-by-step explanation:

The first step is to find the length of BA which is the base, then you have the find the length of CD, the hight.

To find the distance, you need to use the distance formula which is

$d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$ (It does not matter if A is x1 or is B is x1, it just has to remain consistent)

I am going to first find BA

$d=\sqrt{\left({-7}-{-1}\right)^{2}+\left({-1}-{5}\right)^{2}}$

Next, subtract accordingly

$d=\sqrt{\left({-7}+{1}\right)^{2}+\left({-1}-{5}\right)^{2}}$

$d=\sqrt{\left({-6}\right)^{2}+\left({-6}\right)^{2}}$

Once you do that, you want to square -6 and -6 which will give you

$d=\sqrt{\left({36}\right)+\left({36}\right)}$

Now add 36 with 36 which will leave you with

$d=\sqrt{{72}}$

Do that same thing for CD. If you did it right, you should be left with

$d=\sqrt{{18}}$

to find the area of a triangle, you must use the formula

$A=\frac{B*H}{2}$

The Base is $\sqrt{{72}}$ (BA) and the Hight is $\sqrt{{18}}$ (CD). substitute to get

$A=\frac{\sqrt{{72}}*\sqrt{{18}}}{2}$

Multiply the Base by the Hight to get

$A=\frac{\sqrt{{1,296}}}{2}$

Divide 1,296 by 2 to get

$A=\sqrt{{648}}$

Which is equal to

$A=25.455844122715710878430397035775$

Rounding it to the nearest whole number you get

A=25

Hope this helps. Feel free to ask any follow-up questions.

Have a good day! :)

6 0

3 years ago

Amelia is looking at the top of a lighthouse. She knows she is 30 feet from the base of

statuscvo [17]

Answer:

25.7 feet

Step-by-step explanation:

We are solving a right angled triangle.

We are the Trigonometric function of Tangent

tan θ = Opposite side/Adjacent

Angle of Elevation = θ = 34°

Opposite side = Height

Adjacent = 30 feet

tan 34° = Opposite side/30 feet.

Opposite side = tan 34° × 30 feet

Opposite side = 20.235255505 feet

The height of the light house =

Opposite side(height) + Amelia's height

20.235255505 feet + 5.5 feet

= 25.735255505 feet

Approximately to the nearest tenth ≈ 25.7 feet

8 0

3 years ago

Hey guys! I need help with this question.

SSSSS [86.1K]

(a - 8)

liczę na naj

6 0

2 years ago

Evaluate 5.45×1.5/0.025 leave your answer in standard form

malfutka [58]

= 5.45 × 1.5/0.025
= 5.45 x 60
= 327

Answer= 327

Hope this helps! :)

3 0

2 years ago

I need help with this problem please help me

tatiyna

One square root of two plus nine square roots of two equals ten square roots of two.

$\sqrt 2 + 9 \sqrt 2$

$= 1 \sqrt 2 + 9 \sqrt 2$

$=(1 + 9)\sqrt 2$

$=10 \sqrt 2$

Answer: 10√2

6 0

3 years ago