Question

If $2,3$ are the roots of $2x^3+m{x}^2-13x+n=0$, then the values of $m$ and $n$ are, respectively

• A. $-5,-30$
• B. $-5,30$
• C. $5,30$
• D. none

Answer 1

Answer: (B)

$-5,30$

Given, $2x^3+m{x}^2-13x+n=0$

As $2$ is root then substituting $x=2$, we get

${2.2}^3+m{.2}^2-13.2+n=0\Rightarrow 16+4m-26+n=0$
$\Rightarrow 4m+n=10$ ...(1)

And as $3$ is root, then substituting $x=3$, we get
${2.3}^3+m{.3}^2-13.3+n=0\Rightarrow 54+9m-39+n=0$

$\Rightarrow 9m+n=-15$ ...(2)

Solving (1) and (2), we get

$m=-5,n=30$

Hence, option 'B' is correct.