Question

For what value of k will $\frac{7}{3}$ be a root of $3x^2-13x-k=0$

• A. 14
• B. $\frac{3}{7}$
• C. $\frac{-7}{2}$
• D. -14

Answer 1

The correct option is D -14

$p\left(x\right)=3x^2-13x-k$

If $\frac{7}{3}$ is a root of $p\left(x\right)$, then $p\left(\frac{7}{3}\right)=0$

So,$p\left(\frac{7}{3}\right)=3(\frac{7}{3}{)}^2-13(\frac{7}{3})-k=0$

$\therefore k=3(\frac{7}{3}{)}^2-13(\frac{7}{3})=-14$

So, the answer is option (D)