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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

You roll four six-sided die. Find the probability that exactly three of the dice are odd.

s344n2d4d5 [400]

Answer:

3/8

Step-by-step explanation:

There is a 1/2 probability one die will be odd because 1, 3, and 5 are the only possible odd numbers.

Since you want 3/4 of the dice to be odd, you multiply 1/2 by 3/4 to get 3/8.

I believe it is 3/8.

3 0

3 years ago

Read 2 more answers

Can someone help me please.

Ket [755]

Answer:

28. the second and third one

29. 687.50 dollars

Step-by-step explanation:

2.49(2) + 1.79(2) + 0.89(4) = 12.12 no

2.49(3) + 1.79(2) = 11.05 yes

2.49(2) + 1.79(3) + 0.89 = 11.24 yes

2.49(4) + 1.79 + 0.89 = 12.64 no

area = length times width

a = 6.25 times 5

a = 31.25 square feet

31.25(22) = 687.50

3 0

3 years ago

I really need help with this one please

natka813 [3]

The distance from the sun is option 2 5.59 astronomical units.

Step-by-step explanation:

Step 1; To solve the question we need two variables. P which represents the number of years a planet takes to complete a revolution around the Sun. This is given as 13.2 years in the question so P = 13.2 years. The other variable is the distance between the planet and the sun in astronomical units. We need to determine the value of this using the given equation.

Step 2; So we have to calculate the value of 'a' in Kepler's equation. But the exponential power $\frac{3}{2}$ is on the variable we need to find so we multiply both the sides by an exponential power of $\frac{2}{3}$ to be able to calculate 'a'.

P = $a^{\frac{3}{2} }$ , $P^{\frac{2}{3} }$ = $a^{\frac{3}{2}*\frac{2}{3} }$ , $P^{\frac{2}{3} }$ = a, $13.2^{\frac{2}{3} }$ = a = 5.58533 astronomical units.