Question

Given quadratic equations $x^2+5x+p=0\&2x^2+qx+12=0$ have both roots common, then $p+q=$

• A. $22$
• B. $16$
• C. $10$

Answer 1

The correct option is B $16$

Given two quadratic equations:
$x^2+5x+p=0\cdots \left(a\right)$
$\&2x^2+qx+12=0\cdots \left(b\right)$ have two common roots.
Thus, the ratio of corresponding coefficients will be equal
$\Rightarrow \frac{1}{2}=\frac{5}{q}=\frac{p}{12}$
$\Rightarrow q=10\&p=6\Rightarrow p+q=16$