Get A+ with YaClass!
Register now to understand any school subject with ease and get great results on your exams!

### Theory:

The formula for finding the roots of the quadratic equation $$ax^2 + bx + c = 0$$ is:

$x=\frac{-b±\sqrt{{b}^{2}-4\mathit{ac}}}{2a}$

This formula is known as the quadratic formula.
Example:
Find the roots of $$2x^2 + 3x - 77 = 0$$ by using quadratic formula.

Solution:

The given equation is $$2x^2 + 3x - 77 = 0$$.

Here, $$a = 2$$, $$b = 3$$ and $$c = -77$$.

$x=\frac{-b±\sqrt{{b}^{2}-4\mathit{ac}}}{2a}$

Substitute the given values in the formula.

$x=\frac{-3±\sqrt{{3}^{2}-4×2×\left(-77\right)}}{2×2}$

$x=\frac{-3±\sqrt{9+616}}{4}$

$x=\frac{-3±\sqrt{625}}{4}$

$x=\frac{-3±25}{4}$

$x=\frac{-3+25}{4}$ or $x=\frac{-3-25}{4}$

$x=\frac{22}{4}$ or $x=\frac{-28}{4}$

$$x =$$ $\frac{11}{2}$ or $$x = -7$$

Therefore, the roots of the given equation are $$-7$$ and $\frac{11}{2}$.