Question

The value of $a$ for which the equations $x^2-3x+a=0$ and $x^2+ax-3=0$ have a common root is

• A. $2$
• B. $-2$
• C. $3$
• D. $1$

Answer 1

The correct option is A

$2$

Given equations are $x^2–3x+a=0$ …… (i)

and $x^2+ax–3=0$ …… (ii)

Subtract (ii) from (i), we get
$-3x-ax+a+3=0$
$(a+3)(-x+1)=0$

$\Rightarrow$ either $a=–3$ or $x=1$

When $a=–3$, the two equations are identical. So, we take $x=1$,

which is the common root of the two equations.

Substituting $x=1$ in (ii), we get $1+a-3=0$ $\Rightarrow$ $a=2$