Mathematics - Quadratic Equation Question with Solution | TestHub

$b^2=ac$

If $a=0$, then $b=0$ a contradiction ( $\because a\ne 0$ similarly $b\ne 0$ ) If $a\ne 0$, then $c=\frac{b^2}{a}$

On putting in the given relation $a+b+\frac{b^2}{a}=xb\Rightarrow x=\frac{a}{b}+\frac{b}{a}+1$

Now $\frac{a}{b}+\frac{b}{a}\ge 2$ or $\le -2\Rightarrow x\ge 3$ or $\le -3$

But as $x$ has to be positive, $x$ must be $\ge 3$

But $x=3$ when $a=b(a\ne b$ is given $)$

$\Rightarrow x$ should be integer greater than 3 .

$\Rightarrow x=4$