Question

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

Answer 1

Answer:

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

Step-by-step 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