Question

It is given that -1 is one of the zeros of the polynomial $x^3+2x^2-11x-12$. Find all the zeros of the given polynomial.

Answer 1

One zero of the polynomial $x^3+2x^2-11x-12$ is -1

Therefore, $x+1$ is a factor of $x^3+2x^2–11x–12$

Dividing $x^3+2x^2–11x–12byx+1$

Quotient $q\left(x\right)=x^2+x–12$

$=x^2+4x–3x–12$

$=(x+4)(x–3)$

Other zeros of given polynomial are the zeros of q(x)

Therefore, $q\left(x\right)=0$

⇒ $(x+4)(x–3)=0$

⇒ Either $x+4=0orx–3=0$

⇒ Either $x=-4orx=3$

Therefore, -4, 3 are the zeros of q(x)

Therefore, The zeros of given polynomial are -4, -1 and 3