Question

Which of the following is a polynomial with roots 3,5i, and -5i​

f(x)=x^3-3x^2+25x-75

f(x)=x^3-3x^2+15x-25

f(x)=x^3-15x^2+25x-75

f(x)=x^3-3x^2+15x-75

Answer 1

f(x)=x^3-3x^2+25x-75

Explanation:

Solve for x:

x^3 - 3 x^2 + 25 x - 75 = 0

The left hand side factors into a product with two terms:

(x - 3) (x^2 + 25) = 0

Split into two equations:

x - 3 = 0 or x^2 + 25 = 0

Add 3 to both sides:

x = 3 or x^2 + 25 = 0

Subtract 25 from both sides:

x = 3 or x^2 = -25

Take the square root of both sides:

Answer: x = 3 or x = 5 i or x = -5 i