Question

Find the value of $k$ for which the roots of the equation $3x^2-10x+k=0$ are reciprocal of each other.

Answer 1

Let the roots be $\alpha ,\frac{1}{\alpha }$

For a Quadratic Equation $a{x}^2+bx+c=0$

Sum of Roots is given by $\frac{-b}{a}$

$⟹\alpha +\frac{1}{\alpha }=\frac{+10}{3}$

$\frac{-b}{a}=\frac{10}{3}$

From $\left(1\right)⟹a=k=3$