Question

Find the common root of the given quadratic equations.
$x^2-4=0and{x}^2-5x+6=0$

• A. 2

Answer 1

The correct option is A 2
Using the identity : $a^2-b^2$ = $(a-b)(a+b),$
$x^2-4$ = $(x-2)(x+2$)
Hence, $x=2,-2$ are the roots of $x^2-4=0.$

Given equation is $x^2-5x+6=0.$

On comparing with the standard form, $a=1,b=-5$ and $c=6.$
Find the factor pair of $a\times c$ such that the numbers add up to $b.$
$a\times c=6$

Let's consider numbers -2 and -3.
$(-3)\times (-2)=6=a\times c$
$(-3)+(-2)=-5=b$

We now simplify the given equation,
$x^2-5x+6=0$
$\Rightarrow x^2-2x-3x+6=0$
$\Rightarrow x(x-2)-3(x-2)=0$
$\Rightarrow (x-2)(x-3)=0$
$\Rightarrow x=2$ and $x=3$
$\therefore$ 2 and 3 are the roots of the given equation.

So, the common root of both the quadratic equations is 2.