Mathematics | MHT CET 2020 | Discussion Page

The quadratic equation whose roots are the numbers having arithmetic mean 34 and geometric mean 16 is

$x^{2}+68x+256=0$

$x^{2}+68x-256=0$

$x^{2}-68x+256=0$

$x^{2}-68x-256=0$

Option C

Let $\alpha$ and $\beta$ are roots of quadratic equatuion

Given, $\frac{\alpha+\beta}{2}=34$

$\alpha+\beta=68$

and $\sqrt{\alpha\beta}=16$

$\alpha\beta=256$

$\therefore$ Required quadratic equation is,

$x^{2}-(\alpha+\beta)x+\alpha\beta=0$

$x^{2}-68x+256=0$

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