Question

If equation $a{x}^2+2cx+b=0$ and $a{x}^2+2bx+c=0$ have one root in common, then $a+4b+4c$ equals

• A. $0$
• B. $1$
• C. $-1$
• D. $-2$

Answer 1

The correct option is A

$0$

Given: $a{x}^2+2cx+b=0$ and $a{x}^2+2bx+c=0$ have a common root.

Let the common root be $\alpha$.

$\Rightarrow a{\alpha }^2+2c\alpha +b=0$ and $a{\alpha }^2+2b\alpha +c=0$

Subtracting both the equations,
$\alpha (2c-2b)+b-c=0$

$\Rightarrow \alpha =\frac{1}{2}$

Substituting $\alpha =\frac{1}{2}$ in $a{\alpha }^2+2c\alpha +b=0$, we get

$\frac{a}{4}+2c\times \frac{1}{2}+b=0$

$\Rightarrow a+4b+4c=0$