Question

If $2,3$ are roots of $2x^3+m{x}^2-13x+n=0$, then the other root is:

• A. $4$
• B. $\frac{5}{2}$
• C. $-\frac{5}{2}$
• D. $3$

Answer 1

The correct option is C $-\frac{5}{2}$

As $2,3$ are two roots of $2x^3+m{x}^2-13x+n=0$
Let $\alpha$ be third roots, then
$s_2=2.3+2.\alpha +3.\alpha =-\frac{13}{2}\Rightarrow 5\alpha =-\frac{13}{2}-6=-\frac{25}{2}$

$\Rightarrow \alpha =-\frac{5}{2}$