Question

If $\alpha$ and $\beta$ are the zero of the quadratic polynomial find the value of $\frac{1}{\alpha }+\frac{1}{\beta }-\alpha \beta$.

Answer 1

considering the quadratic equation to be:

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

$\alpha +\alpha =\frac{-b}{a}$

$\alpha \beta =\frac{c}{a}$

given,

$\frac{1}{\alpha }+\frac{1}{\beta }-\alpha \beta$

$=\frac{\alpha +\beta }{\alpha \beta }-\alpha \beta$

$=\frac{\frac{-b}{a}}{\frac{c}{a}}-\frac{c}{a}$

$=\frac{-b}{c}-\frac{c}{a}$

$=-\frac{ab+c^2}{ac}$