Question

If $x^2+3x+1=0$, Then the roots of the equation are $x=\frac{-3\pm M}{2}$.what is the value of $M$?

Answer 1

Compute the required value.

A quadratic equation $x^2+3x+1=0$ is given.

Find the roots of the quadratic equation by using the quadratic formula.

If a quadratic equation is in the form of $a{x}^2+bx+c=0$.

Then, according to the quadratic formula, $\mathbf{x}\mathbf{=}\frac{\mathbf{-}\mathbf{b}\mathbf{\pm }\sqrt{{\mathbf{b}}^{\mathbf{2}}\mathbf{-}\mathbf{4}\mathbf{ac}}}{\mathbf{2}\mathbf{a}}$.

Therfore,

$$\begin{gathered} x=\frac{-3\pm \sqrt{9-4}}{2} \\ \Rightarrow x=\frac{-3\pm \sqrt{5}}{2}...1 \end{gathered}$$

Also, it is given that, $x=\frac{-3\pm M}{2}...2$

On comparing equation $1$ and equation $2$ we get,

$M=\sqrt{5}$.

Hence, the value of $M$ is $\sqrt{5}$.