Question

If AM and GM of roots of a quadratic equation are 8 and 5 respectively, then obtain the quadratic equation.

Answer 1

Let quadratic equation be $(x-\alpha )(x-\beta )=0$

Roots are $\alpha ,\beta$

Here,

$\frac{\alpha +\beta }{2}=8,\sqrt{\alpha \beta }=5$

$\alpha +\beta =16,\alpha \beta =25$

$\therefore$ Required quadratic equation is,

$x^2-16x+25=0$