# How do you simplify the quadratic formula?

Dec 27, 2017

A few thoughts...

#### Explanation:

If you are wanting simpler versions of the quadratic formula, then here are a few thoughts...

Given a quadratic equation of the form:

$a {x}^{2} + b x + c = 0$

the roots are given by the quadratic formula:

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

Note that if $b$ is even, then the radicand ${b}^{2} - 4 a c$ is a multiple of $4$, so we end up with a square root that can be simplified.

We can incorporate this simplification into a simplified quadratic formula for the equation:

$a {x}^{2} + 2 \mathrm{dx} + c = 0$

namely:

$x = \frac{- d \pm \sqrt{{d}^{2} - a c}}{a}$

Further note that if (as is commonly the case) $a = 1$, then the roots of:

${x}^{2} + 2 \mathrm{dx} + c = 0$

are:

$x = - d \pm \sqrt{{d}^{2} - c}$