The A.M. of the roots of a quadratic equation is A and G.M. of its roots is G. The quadratic equation is

Question

The A.M. of the roots of a quadratic equation is $A$ and G.M. of its roots is $G$ . The quadratic equation is

Smart Achievers · Accepted Answer

(4)

$Let the equation be$ $x^{2} - (α + β) x + α β = 0 has roots α, β .$

$Also, A = \frac{α + β}{2}, G = \sqrt{α β}$ $\Rightarrow α + β = 2 A,$ $α β = G^{2}$

$∴$ $The required equation is x^{2} - 2 A x + G^{2} = 0$

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