Question

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

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

Answer 1

The correct option is C -3 and -2

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.