Question

The roots of the quadratic equation $3x^2-kx+14=0$ are in the ratio $7:6$, then $k$ equals _________.

• A. $13$
• B. $12$
• C. $1$
• D. $-3$

Answer 1

The correct option is A $13$

Let $p,q$ be the roots of the given quadratic equation $3x^2-kx+14=0$

$\Rightarrow$ Sum of the roots $=p+q=k/3\to \left(I\right)$

and Product of the roots $=pq=14/3\to \left(II\right)$

We also know $\frac{p}{q}=\frac{7}{6}$

$\Rightarrow p=\frac{7q}{6}\to \left(III\right)$

Substituting $\left(III\right)$ in $\left(II\right)$ we get,

$\frac{7q^2}{6}=\frac{14}{3}$

$\Rightarrow q^2=4$

$\Rightarrow q=2$

$\Rightarrow p=\frac{7\times 2}{6}=\frac{7}{3}$

Substituting values of $p,q$ in $\left(I\right)$ we get,

$\frac{7}{3}+2=\frac{k}{3}$

$\Rightarrow \frac{k}{3}=\frac{13}{3}$

$\Rightarrow k=13$