Class 11

Math

Algebra

Sequences and Series

Write the quadratic equation, the arithmetic and geometric means of whose roots are A and G respectively.

Let the roots of the quadratic equation be $α$ and $β$.

Then, the equation is $(x_{2}−(α+β)x+αβ=0$

$∴A=2α+β $

$⇒α+β=2A$

$g=αβ $

$⇒αβ=G_{2}$.

Hence, the required equation is $x_{2}−2Ax+G_{2}=0$.