Question

The roots of the quadratic equation $x^2-5x+6=0$ are .

• A. 2 and 3
• B. 1 and 6
• C. -2 and -3
• D. -1 and -6

Answer 1

The correct option is A 2 and 3

Given equation is $x^2-5x+6=0.$
Standard form of a quadratic equation is $a{x}^2+bx+c=0$
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 $b.$
$a\times c=6$
Factor pairs of 6 are $1\times 6,2\times 3,-1\times -6,-2\times -3$
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.