How do you simplify the quadratic formula?

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Answer 1 · 2017-12-27T00:43:00

A few thoughts...

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

Given a quadratic equation of the form:

#ax^2+bx+c = 0#

the roots are given by the quadratic formula:

#x = (-b+-sqrt(b^2-4ac))/(2a)#

Note that if #b# is even, then the radicand #b^2-4ac# 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:

#ax^2+2dx+c = 0#

namely:

#x = (-d+-sqrt(d^2-ac))/a#

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

#x^2+2dx+c=0#

are:

#x = -d+-sqrt(d^2-c)#