Question

1. If x³ +3x²-4=0 has x=-2 as a root (zero), find the other two roots.

Answer 1

1 and -2 (has a multiplicity of 2)

Explanation:

so since x=-2 is a root then (x+2) is a factor of the polynomial. This means you can divide the polynomial by (x+2) by using synthetic or long division. So for this example I'll using synthetic division which is much more simple than long division

-2 | 1 3 0 -4

-2 -2 4

1 1 -2 0

(x+2)(x²+x-2)

Now you can factor the quadratic into

(x+2)(x-1)

x+2 = 0

x = - 2

x-1 =0

x = 1