Question

Find the zeros of the following

please solve step by step
1. x³+x²-4x-4=0
2. 2x³-11x²+17x-6=0

Answer 1

Question 1

`x^3 + x^2 - 4x-4=0\\\\x^2 (x+1)-4(x+1)=0\\\\(x^2 -4)(x+1)=0\\\\(x-2)(x+2)(x+1)=0\\\\x=-2, -1, 2`

Question 2

By inspection, we know that
`x=2` is a root.

`(2x^3 - 11x^2 + 17x-6)/(x-2)=2x^2 - 7x+3`.

So, we can factor the equation as

`(x-2)(2x^2 - 7x+3)=0\\\\(x-2)(x-3)(2x-1)=0\\\\x=(1)/(2), 2, 3`