Question

The quadratic equation having roots as $a\&b$ is (Where A and G are arithmetic and geometric mean of $a$ and $b$

• A. $x^2-2Gx+A=0$
• B. $x^2-2Ax+G^2=0$
• C. $x^2+2Ax+G=0$
• D. $x^2-Ax+2G=0$

Answer 1

The correct option is B $x^2-2Ax+G^2=0$

Given: Roots are $a$ and $b$

Sum of the roots $=a+b$

Product of the roots $=ab$

Quadratic equation having $a$ and $b$ as it's roots is
$x^2-\text{Sum of the roots}\times x+\text{Product of the roots}=0$

$\Rightarrow x^2-(a+b)x+ab=0$

As we know, $A=\frac{a+b}{2},G^2=ab$

$\therefore x^2-2Ax+G^2=0$