Question

The set of roots of the quadratic equation $x^2-8x+12=0$ is

• A. $\{3,6\}$
• B. $\{2,6\}$
• C. $\{2,8\}$
• D. $\{3,8\}$

Answer 1

The correct option is B $\{2,6\}$

Given: $x^2-8x+12=0$
Let $\alpha ,\beta$ be the roots of the equation $a{x}^2+bx+c=0$
$\Rightarrow \alpha =\frac{-b+\sqrt{D}}{2a}$

$\&\beta =\frac{-b-\sqrt{D}}{2a}$
$D=b^2-4ac$ is the discriminant of the equation.
Here, $D=64-4\left(1\right)\left(12\right)=16$
$\Rightarrow \sqrt{D}=4$
$\therefore \alpha =\frac{8+4}{2\times 1}=6\&\beta =\frac{8-4}{2\times 1}=2$