Question

If the equation $a{x}^2+2bx+c=0$ and $a{x}^2+2cx+b=0,b\ne c$, have a common root, then find the value of $\frac{a}{b+c}$.

• A. $-4$
• B. $3$
• C. $7$
• D. $4$

Answer 1

The correct option is A $-4$

$a{x}^2+2bx+c=0$
$a{x}^2+2cx+b=0$
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$\frac{x^2}{2(b^2-x^2)}=\frac{x}{(c-b)a}=\frac{1}{2a(c-b)}$
$\Rightarrow x=\frac{1}{2}$ is the common root
Put $x=\frac{1}{2}$ in the equation $a{x}^2+2bx+c=0$
$\Rightarrow \frac{a}{4}+b+c=0$
$\Rightarrow \frac{a}{b+c}=-4$