Question

If the A.M. and G.M. of roots of a quadratic equations are 8 and 5 respectively, then the quadratic equation will be

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Given that A.M. = 8 and G.M. = 5, if $\alpha ,\beta$ are roots of quadratic equation, then quadratic equation is
$x^2-x(\alpha +\beta )+\alpha \beta =0$ ......(i)
$A.M.=\frac{\alpha +\beta }{2}=8\Rightarrow \alpha +\beta =16$ ....(ii)
and $G.M.=\sqrt{\alpha \beta }=5\Rightarrow \alpha \beta =25$ ....(ii)
So the required quadratic equation will be $x^2-16x+25=0$.