Write the quadration the arithmetic and geometric means of whose … - Vidyadip

Question

Write the quadration the arithmetic and geometric means of whose roots are A and G respectively.

✓

Answer

Let $\alpha,\beta, $ be roots of equation, so equation is
$\text{x}^2-(\alpha+\beta)\text{x}+\alpha\beta=0$
Here,
$\frac{\alpha+\beta}{2}=\text{A}$
$\alpha+\beta=2\text{A}$
And $\sqrt{\alpha\beta}=\text{G}$
$\alpha\beta=\text{G}^2$
So, Required equation is,
$\text{x}^2-2\text{Ax}+\text{G}^2=0$

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