Question

Match the quadratic equations with their respective roots.

• A. -3 and -2
• B. -3 and -5
• C. -3 and 2

Answer 1

Consider the quadratic equation $x^2+8x+15=0.$
Comparing the given equation with thee standard form $a{x}^2+bx+c=0,$ where $a,b$ and $c$ are constants ($a\ne 0$), we have
$a=1,b=8$ and $c=15.$
Consider the product of $a$ and $c.$
$a\times c=1\times 15=15$
Factorising $a\times c$ such that the numbers add up to $b$
$\Rightarrow b=8=5+3$
Hence, the quadratic equation can be written as $x^2+5x+3x+15=0.$
$\Rightarrow (x+5)(x+3)=0$
$\Rightarrow x=-5,-3$ are the roots of the equation.

Similarly, $x^2+5x+6=0$ will have 2 and 3 as factors of 6(i.e.,a$\times$c) such that their sum is 5.
$\Rightarrow (x+2)(x+3)=0$
$\Rightarrow x=-2,-3$ are the roots of the equation.

Similarly, $x^2+x-6=0$ will have 3 and -2 as factors of -6(i.e.,a$\times$c) and their sum is 1.
$\Rightarrow (x-2)(x+3)=0$
$\Rightarrow x=2,-3$ are the roots of the equation.