Question

If A.M and G.M of the roots of a quadratic equation are $10$ and $8$ respectively , then obtain the quadratic equation .

Answer 1

Let roots are $\alpha$ & $\beta$

then $\left(\frac{\alpha +\beta }{2}\right)=ArithmeticMean=10$

$\therefore \alpha +\beta =20$

$and\sqrt{\alpha \beta }=GeometricMean=8$

$\therefore \alpha \beta =64$

now quadratic equation can be written as:

$x^2-(\alpha +\beta )x+\left(\alpha \beta \right)=0$

$x^2-20x+64=0$