Question

If $\alpha$, $\beta$ are the roots of the equation $x^2-5x+6=0$, the value of ${\alpha }^2-{\beta }^2$ is:

• A. $\pm 5$
• B. $\pm 13$
• C. $\pm 6$
• D. $\pm 7$

Answer 1

The correct option is A $\pm 5$

Given quadratic equation $x^2-5x+6=0$
$\therefore$ a = 1, b = -5, c = 6

$\therefore x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
$\Rightarrow x=\frac{-(-5)\pm \sqrt{(-5{)}^2-4(1\left)\right(6)}}{2\left(1\right)}$
$\Rightarrow x=\frac{5\pm \sqrt{25-24}}{2}$
$\Rightarrow x=\frac{5\pm 1}{2}$
$\Rightarrow x=3,2$

If $\alpha$, $\beta$ is 3,2 , then ${\alpha }^2-{\beta }^2=9-4=5$
If $\alpha$, $\beta$ is 2,3 , then ${\alpha }^2-{\beta }^2=4-9=-5$