Question

Find a quadratic polynomial whose zeroes are $\frac{1}{\alpha }$ and $\frac{1}{\beta }$. If $\alpha$ and $\beta$ are the zeroes of $2x^2-3x+5$

Answer 1

Given $\alpha ,\beta$ are the roots of $2x^2-3x+5=0\cdots \left(1\right)$

To get the quadratic equation whose roots are $\frac{1}{\alpha },\frac{1}{\beta }$

Replace $x$ by $\frac{1}{x}$ in $\left(1\right)$

$⟹\frac{2}{x^2}-\frac{3}{x}+5=0⟹5x^2-3x+2=0$