Question

Write a cubic polynomial in standard form which has zeros of 5 and -3 only. The larger root occurs twice.

Answer 1

Hello from MrBillDoesMath

Answer: x^3 - 7x^2 - 5x + 75

Discussion:

The cubic polynomial has factors (x-5) and (x - ( -3)). The larger root, 5, occurs twice mean the actual polynomial factorization is:

(x-5)^2 * (x+3) =>

(x^2 -10x +25) * (x +3) =

( x^2 -10x +25) * x + ( x^2 -10x +25) * 3 =

(x^3 - 10x^2 + 25 x) + (3x^2 - 30x + 75) = (combine similar terms)

x^3 + x^2 ( -10 +3) + + x (25 -30) + 75 =

x^3 - 7x^2 - 5x + 75

Thank you,

Mr. B