How do you simplify the quadratic formula?

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How do you simplify the quadratic formula?

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Answer 1 · 2017-12-27T00:43:00

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:

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

the roots are given by the quadratic formula:

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ $x = (-b+-sqrt(b^2-4ac))/(2a)$

Note that if $b$ $b$ is even, then the radicand $b^{2} - 4 a c$ $b^2-4ac$ is a multiple of $4$ $4$ , 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:

$a x^{2} + 2 d x + c = 0$ $ax^2+2dx+c = 0$

namely:

$x = \frac{- d \pm \sqrt{d^{2} - a c}}{a}$ $x = (-d+-sqrt(d^2-ac))/a$

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

$x^{2} + 2 d x + c = 0$ $x^2+2dx+c=0$

are:

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

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How do you simplify the quadratic formula?

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