Question

If one root of $5x^2+13x+k=0$ is reciprocal of the other then $k=$

• A. $0$
• B. $5$
• C. $\frac{1}{6}$
• D. $6$

Answer 1

Answer: (B)

$5$

$5x^2+13x+k=0\therefore a=5,b=3,c=k$

Let one root be $\alpha$
$\therefore$ Other root will be $\frac{1}{\alpha }$
$\therefore$ Product of roots = $\frac{c}{a}$ $\Rightarrow \alpha \times \frac{1}{\alpha }=\frac{k}{5}\Rightarrow 5\times 1=k$ $\therefore$ k = 5