Question

Equation $x^2+5x-7=0$ has roots a and b. Equation $2x^2+px+q=0$ has roots $a+1$ and $b+1$. Find $p+q$.

• A. 6
• B. 0
• C. -16
• D. 2

Answer 1

The correct option is C -16

Given that equation $x^2+5x-7=0$ has roots $a$ and $b$

So we get $a+b=-5$ and $ab=-7$

The roots of equation $2x^2+px+q=0$ is $a+1,b+1$

So we get $a+b+2=-\frac{p}{2}$

$\Rightarrow p=-2(-5+2)=6$

From product of roots we get $\frac{q}{2}=(a+1)(b+1)=ab+a+b+1=-11$

$\Rightarrow q=-22$

Therefore $p+q=6-22=-16$

So the correct option is $C$