Question

If two roots of $x^3-9x^2+14x+24=0$ are in the ratio $3:2$ then the roots are

• A. $6,4,-1$
• B. $3,2,4$
• C. $-6,4,1$
• D. $6,4,2$

Answer 1

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

$f\left(x\right)=x^3-9x^2+14x+24$

$f(-1)=-1-9-14+24$

$f(-1)=0$

As,$f(-1)=0$

$\therefore (x+1)$ is a factor of $f\left(x\right)$

$f\left(x\right)=(x+1)(x^2-10x+24)$

$f\left(x\right)=(x+1)(x-6)(x-4)$

$f\left(x\right)=0$

$\therefore x=-1,4,6$