Question

$s=\frac{1}{\alpha }+\frac{1}{\beta }=\frac{\alpha +\beta }{\alpha \beta }=\frac{\frac{-b}{a}}{\frac{c}{a}}=-\frac{b}{a}$ and $P=\frac{1}{\alpha }\times \frac{1}{\beta }=\frac{1}{\alpha \beta }=\frac{1}{\frac{c}{a}}=\frac{a}{c}$
Hence ,the required polynomial g(x) is given by
$g\left(x\right)=k\left(x^2-Sx+P\right)=k\left(x^2+\frac{bx}{c}+\frac{a}{c}\right),$ where k is any non-zero constant.

Answer 1

$\frac{1}{\alpha },\frac{1}{\beta }$ are the zeroes of $k(x^2-(\frac{1}{\alpha }+\frac{1}{\beta })x+\frac{1}{\alpha \beta })$

$⟹g\left(x\right)=k(x^2-Sx+P)$