Find the roots of polynomialgiven that x+1 is a factor. f(x)=x x ^(4) - 3x^(3 ) - 7x ^(2) + 9x + 12 ​

Question

Find the roots of polynomialgiven that x+1 is a factor.

f(x)=x

`x ^(4) - 3x^(3 ) - 7x ^(2) + 9x + 12`
​

Answer 1

Explanation:

since it's given that (x +1) is a factor, f (-1) = 1

now let's divide f (x) by ( x + 1 )

(you can use the long division method )

then u get x^3 - 4x^2 - 3x + 12

now let's factorize this

x^3 - 4x^2 - 3x + 12

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

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

x = +- sqrt 3 / x = 4 and x = -1