# If x = 1 is a common root of ax2 + ax + 2 = 0 and x2 + x + b = 0, then, ab =

Question:

If $x=1$ is a common root of $a x^{2}+a x+2=0$ and $x^{2}+x+b=0$, then, $a b=$

(a) 1
(b) 2
(c) 4
(d) 3

Solution:

$x=1$ is the common roots given quadric equation are $a x^{2}+a x+2=0$, and $x^{2}+x+b=0$

Then find the value of $a b$.

Here, $a x^{2}+a x+2=0$.........(1)

$x^{2}+x+b=0$......(2)

Putting the value of $x=1$ in equation (2) we get

$1^{2}+1+b=0$

$2+b=0$

$b=-2$

Now, putting the value of $x=1$ in equation (1) we get

$a+a+2=0$

$2 a+2=0$

$a=\frac{-2}{2}$

$=-1$

$a b=(-1) \times(-2)$

Then,

$=2$

Thus, the correct answer is (b)