Question 200465: Quadratic equation: Why do you think the discriminant works.
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! The Quadratic Formula is the answer to
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ax^2 +bx + c =0,,,,,, most books have a derivation
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as to why the Discriminant (D) works, let's look at quadratic answer
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x= [ - (b) +/- sqrt { (b^2) - 4 (a) (c) } ] / 2a
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or,,,,x= [-(b) +/- sqrt D ] / 2a
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there are 3 conditions for the discriminant (D)
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(1) D =0,,,,then x=[ -(b) +/- sqrt(0) ] /2a = -b/2a,,,,,therefore one answer
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(2) D>0,,,,,,then x= [ -(b) +/- sqrt D ] /2a or x= [-(b) + sqrtD]/2a,,and x = [-b -sqrtD] /2a,,, or two answers
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(3) D less than 0,,,,,,then x=[ -(b) +/- sqrt D ] /2a = [-b +/-sqrt (-#) ] /2a ,,,and with sqrt of a negative number, the answer is a complex number, not a real number,,,,,,therefore NO real number answers
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