Friday, 22 April 2016

calculus - Quadratic Formula Returns Different Root Signs



My question is as follows:



I am currently working on a problem set for "Integration of Rational Functions By Partial Fractions" and I came across the following problem:




1022x2+3x+1dx



Now, the issue I have is with factoring the demoninator.



When I used the quadratic formula:



x=b±b24ac2a



I came up with the roots:




(x12)(x1)



I then multiplied the left hand root by 2:
(2x1)(x1)



However, when I multiplied out these two roots, I came out with:
2x23x+1



I know I am most likely doing something wrong, but I have looked for other questions similar to this one and I have been having a hard time finding out an accurate explanation of what my error is in this problem.




(edit)



The format for quadratic roots is as follows:
(xa)(xb)



Therefore, if either a or b is negative, then the resulting root would be positive.



As a result, the two roots would therefore be:




(2x+1)(x+1)



Thanks


Answer



HINT: it is 2x2+3x+1=(x+1)(2x+1)


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