Question 200465
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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