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Discussion Forum



1)

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


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

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

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

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

Answer:

Option C

Explanation:

 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,

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

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