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Math Help - question about deriving the quadratic formula

  1. #1
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    question about deriving the quadratic formula

    In a step of the derivation of the quadratic formula, we have plus or minus sqrt(b^2-4ac/(4a^2)) = plus or minus sqrt(b^2 - 4ac)/2a. Basically just took the square root of the bottom of the fraction. My question is, doesnt the a in the denominator of the last expression have to be |a| because we took the square root of a ^2 ? If this is not the case, why not?
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  2. #2
    Senior Member apcalculus's Avatar
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    Quote Originally Posted by eniuqvw View Post
    In a step of the derivation of the quadratic formula, we have plus or minus sqrt(b^2-4ac/(4a^2)) = plus or minus sqrt(b^2 - 4ac)/2a. Basically just took the square root of the bottom of the fraction. My question is, doesnt the a in the denominator of the last expression have to be |a| because we took the square root of a ^2 ? If this is not the case, why not?
    You can always re-write the equation so as to assume a>0 by moving everything to the other side whenever a is negative.
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  3. #3
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    response to apcalculus

    ok so you mean when ax^2 +bx + c = 0 and a is negative, we can multiply the equation by -1 and then the argument holds without the needing absolute values? that makes sense, but to be clear the deduction isn't quite valid without this step.. correct? Thanks for the help
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  4. #4
    Senior Member apcalculus's Avatar
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    correct.
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