Question

Write a polynomial equation of degree 4 that has the following roots : -1 repeated three times and 4

Answer 1

Explanation:

roots = -1, -1, -1, 4

(x + 1)(x + 1)(x + 1)(x - 4) = 0

(x^2 + 2x + 2)(x^2 - 3x - 4) = 0

x^2(x^2 - 3x - 4) + 2x(x^2 - 3x - 4) + 2(x^2 - 3x - 4) = 0

x^4 - 3x^3 - 4x^2 + 2x^3 - 6x^2 - 8x + 2x^2 - 6x - 8 = 0

x^4 - x^3 - 8x^2 - 14x - 8 = 0

Answer 2

x^4 -x^3 -9x^2 -11x -4

Explanation:

We can use the zero product property

(x-a) (x-b) (x-c) (x-d) where a b c d are the roots

(x- -1)(x- -1)(x- -1) ( x-4) since the root -1 is repeated 3 times and 4 is a root

(x+1)(x+1)(x+1) ( x-4)

Foil the first two terms and the last two terms

(x^2 + 2x+1)( x^2 -3x-4)

Foil again

x^4 -3x^3 -4x^2 +2x^3 -6x^2 -8x +x^2 -3x-4

Combine like terms

x^4 -x^3 -9x^2 -11x -4