Question

Q2. If the quadratic equation x² + px + q = 0 and x² + qx + p = 0 ($p\ne q$)have a common root, then the value of p + q is
(1) 1
(2) -1
(3) 2
(4) 0

Answer 1

Dear Student,

$$\begin{gathered} x^2+px+q=0and{x}^2+qx+p=0 \\ \Rightarrow x^2+px+q=x^2+qx+p \\ \Rightarrow px+q=qx+p \\ \Rightarrow \left(p-q\right)x=p-q \\ \Rightarrow \left(p-q\right)x-\left(p-q\right)=0 \\ \Rightarrow \left(p-q\right)\left(x-1\right)=0 \\ Sincep\ne q \\ \Rightarrow x-1=0 \\ \Rightarrow x=1 \\ \Rightarrow 1^2+p+q=0 \\ \Rightarrow p+q=-1 \end{gathered}$$

Regards