Question

If $x^2+3x+1=0$, then the roots of the equation are $x=\frac{-3\pm \sqrt{m}}{2}$.

What is the value of $m$?

Answer 1

Given quadratic equation is: $x^2+3x+1=0$
Applying quadratic formula:

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2}$

$x=\frac{-3\pm \sqrt{9-4}}{2\times 1}$

$x=\frac{-3\pm \sqrt{5}}{2}$

$\therefore$ The roots of the given equation are $\frac{-3\pm \sqrt{5}}{2}$

Hence, the value of $m$ is $5$.