Thank you for reporting, we will resolve it shortly
Q.
If A.M. and G.M. of roots of a quadratic equation are 8 and 5 , respectively, then quadratic equation is
Sequences and Series
Solution:
Let the roots of the quadratic equation are $\alpha$ and $\beta$, then (arithmetic mean) $\frac{\alpha+\beta}{2}=8$ and (geometric mean) $\sqrt{\alpha \beta}=5$
$\Rightarrow \alpha+\beta=16$ and $\alpha \beta=25$
Now, if roots are $\alpha$ and $\beta$, then quadratic equation is $x^2-$ (sum of roots $) x+$ product of roots $=0$
$\Rightarrow x^2-(\alpha+\beta)+\alpha \beta=0 $
$\Rightarrow x^2-16 x+25=0$