Thread: 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?

Originally Posted by eniuqvw

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.

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

correct.