Question

Match the following quadratic equations with their corresponding roots.

• A. 0 and -8
• B. 1 and 3
• C. 0 and 6

Answer 1

The roots of a quadratic equation $a{x}^2+bx+c=0,$ where $a,b$ and $c$ are constants are given by
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}.$

Consider the equation $x^2+8x=0.$
Here, $a=1,b=8$ and $c=0.$

$\Rightarrow x=\frac{-8\pm \sqrt{(-8{)}^2-4(1\left)\right(0)}}{2\times 1}$

$\Rightarrow x=\frac{-8\pm \sqrt{64}}{2}$

$\Rightarrow x=0,-8$

Consider the equation $x^2-4x+3=0.$
Here, $a=1,b=-4$ and $c=3.$

$\Rightarrow x=\frac{-(-4)\pm \sqrt{(-4{)}^2-4(1\left)\right(3)}}{2\times 1}$

$\Rightarrow x=\frac{4\pm \sqrt{4}}{2}$

$\Rightarrow x=3,1$

Lastly, in the equation $x^2-6x=0,$ we have
$a=1,b=-6$ and $c=0.$

$\Rightarrow x=\frac{-(-6)\pm \sqrt{(-6{)}^2-4(1\left)\right(0)}}{2\times 1}$

$\Rightarrow x=\frac{6\pm \sqrt{36}}{2}$

$\Rightarrow x=6,0$