If the zeroes of the polynomial $a x^{2}+b x+\frac{2 a}{b}$ are reciprocal of each other, then the v

Question

If the zeroes of the polynomial $a x^{2}+b x+\frac{2 a}{b}$ are reciprocal of each other, then the value of $b$ is\

Professor PC Thomas Classes · Answer

(a) : Let $\alpha$ and $\beta$ be the zeroes of the given polynomial $a x_{2}+b x+\frac{2 a}{b}$.\ Given $\beta=\frac{1}{\alpha}$\ ⇒ Product of zeroes $=\alpha \cdot \beta=\frac{	ext { Constant term }}{	ext { Coefficient of } x^{2}}$\ $\Rightarrow \alpha \cdot \frac{1}{\alpha}=\frac{2 a / b}{a} \Rightarrow 1=\frac{2 a}{b 	imes a} \Rightarrow 1=\frac{2}{b} \Rightarrow b=2$