Question

If $c^2=4d$ and the two equations $x^2-ax+b$ and $x^2-cx+d=0$ have one common root, then the value of $2(b+d)$ is equal

• A. $\frac{a}{c}$
• B. ac
• C. 2ac
• D. a+c

Answer 1

The correct option is B ac

Given,

$x^2-cx+d=0$

Let the roots be $\alpha ,\alpha$

$c^2=4d$

$c^2-4d=0$

$\Delta =0$ as roots are equal

$\alpha +\alpha =c$

$\Rightarrow \alpha =\frac{c}{2}$

$\therefore {\alpha }^2=d$

$x^2-ax+b=0$

Let $\alpha$ be the root

${\alpha }^2-\alpha x+b=0$

$d-\frac{ac}{2}+b=0$

$d+b=\frac{ac}{2}$

$2(d+b)=ac$

Hence the result.