Question

The roots of the equation $x^3-9x^2+14x+24=0$, are

• A. $-1,-4,6$
• B. $-1,4,-6$
• C. $-1,-4,-6$
• D. $-1,4,6$

Answer 1

The correct option is D $-1,4,6$

Given equation is $x^3-9x^2+14x+24=0$
Put $x=-1$ in the above equation we get,

$\therefore {(-1)}^3-{9(-1)}^2+14(-1)+24=0$

Hence, $x=-1$ is one root of the equation.

Dividing the given equation by $(x+1)$, we get $x^2-10x+24.$

$\therefore (x+1)(x^2-10x+24)=0$

$\Rightarrow (x+1)(x-4)(x-6)=0$
Hence, roots are $-1,4,6$.