Question

State the following statement is True or False

The zeros of the polynomial $x^4+4x^3-x^2-16x-12$ are $2,-2,-1$ and $-3$

• A. True
• B. False

Answer 1

The correct option is A True

Solution:

Let $p\left(x\right)=x^4+4x^3-x^2-16x-12=(x^2-4)(x^2-4x+3)$

Zeroes of the polynomial $=2,-1,-3$

We know that if $a$ is zero of a polynomial then it must satisfy $p\left(a\right)=0$

Now,

$p\left(2\right)=(4-4)(2^2+4\times 2+3)=0$

$p(-2)=(4-4)\left(\right(-2{)}^2+4\times (-2)+3)=0$

$p(-1)=(1-4)\left(\right(-1{)}^2+4\times (-1)+3)=0$

$p(-3)=(9-4)\left(\right(-3{)}^2+4\times (-3)+3)=0$

Since, $p\left(2\right)=p(-2)=p(-1)=p(-3)=0$

$\therefore 2,-2,-1,$ and $-3$ are zeroes the polynomial $p\left(x\right).$

Hence, A is the correct answer.