Theory Of Equations Ques 3
- If the quadratic equations $x^2+a x+b=0$ and $x^2+b x+a=0 \quad(a \neq b)$ have a common root, then the numerical value of $a+b$ is… .
$(1986,2 M)$
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Answer:
Correct Answer: 3.$(-1)$
Solution: Given equations are $x^2+a x+b=0$ and
$x^2+b x+a=0$ have common root
On subtracting above equations, we get
$\Rightarrow \quad (a-b) x+(b-a) =0 $
$\quad x =1$
$\therefore \quad x=1$ is the common root.
$ \begin{aligned} \Rightarrow \quad & 1+a+b =0 \\ \Rightarrow \quad & a+b =-1 \end{aligned} $
BETA
