If one zero of the polynomial $6 x^{2}+37 x-(k-2)$ is reciprocal of the other, then what is the valu

Question

If one zero of the polynomial $6 x^{2}+37 x-(k-2)$ is reciprocal of the other, then what is the value of $k$ ?\

Professor PC Thomas Classes · Answer

(a) : Let $\alpha$ and $\frac{1}{\alpha}$ be two zeroes of quadratic polynomial $6 x^{2}+37 x-(k-2)$ then $\alpha 	imes \frac{1}{\alpha}=\frac{-(k-2)}{6}$\ $\Rightarrow \quad-k+2=6 \Rightarrow-k=4 \Rightarrow k=-4$\