# Find the roots of the equation: y = -x^2 - 7x - 2.

## Question:

Find the roots of the equation: {eq}y = -x^2 -7x - 2 {/eq}.

## Roots of a Quadratic Equation:

The roots of the equation {eq}y=ax^2+bx+c {/eq} are the values of {eq}x {/eq} such that {eq}ax^2+bx+c=0 {/eq}. The roots of a quadratic equation {eq}ax^2+bx+c=0 {/eq} are given by the formula:

{eq}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a} {/eq}

The roots of {eq}y = -x^2 -7x - 2 {/eq} are the values of {eq}x {/eq} such that {eq}y=0. {/eq}

Hence, to find the roots, we need to solve the quadratic equation {eq}-x^2 -7x - 2=0 {/eq}, that is, {eq}x^2+7x+2=0 {/eq}.

Here we are going to use the formula method for finding the roots.

By that method:

{eq}\begin{align*} x &=\frac{-7\pm \sqrt{7^2-4*1*2}}{2*1}\\ \\ &=\frac{-7\pm \sqrt{49-8}}{2}\\ \\ &=\frac{-7\pm \sqrt{41}}{2} \end{align*} {/eq}

Hence, the required roots are:

{eq}\displaystyle x=\frac{-7+\sqrt{41}}{2} \\ \displaystyle x=\frac{-7-\sqrt{41}}{2} {/eq}