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 (A) x2 +Ax +G2 = 0 (B) x2 + 2Ax +G2 = 0 (C) x2 - Ax +G2 = 0 (D) x2 -2Ax +G2 = 0

Tardigrade Admin · Accepted Answer

Let the equation be x2 - ( α+β)x + αβ = 0 has roots α, β Also, A= (α+β/2), G = √αβ ⇒ α + β = 2 A, αβ= G2 ∴ The required equation is x2 -2 Ax + G2 = 0.

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

$x^{2} + A x + G^{2} = 0$

$x^{2} + 2 A x + G^{2} = 0$

$x^{2} - A x + G^{2} = 0$

$x^{2} - 2 A x + G^{2} = 0$

Let the equation be
$x^{2} - (α + β) x + α β = 0$ has roots $α, β$
Also, $A = \frac{α + β}{2}, G = α β$
$\Rightarrow α + β = 2 A,$ $α β = G^{2}$
$∴$ The required equation is $x^{2} - 2 A x + G^{2} = 0$ .

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

x2+Ax+G2=0

x2+2Ax+G2=0

x2−Ax+G2=0

x2−2Ax+G2=0