the question is find all zeros of f(x)=X^4-5x^2-10x-6

i ofund -1, and 3 are the zeros.

(x+1)(x^3-x^2-4x-6)

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

my question is how do i leave the answer.. do i factor further, and how would i factor that to prove that they are zeros?

## Answers (1)

You're correct as far as you've gone.

Now take the two factors you've found and divide them into the original function, which gives

X^4-5x^2-10x-6/(x+1)(x-3) = x^2 +2x + 2

set that last quadratic to zero and use the quadratic formula:

x = [-2 ± (4 - 8)] / 2 = -1 ± i

where i = √-1

so altogether you have zeros at

x = -1, 3, -1 + i, -1 - i