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±√b2−4ac2a
I came up with the roots:
(x−12)(x−1)
I then multiplied the left hand root by 2:
(2x−1)(x−1)
However, when I multiplied out these two roots, I came out with:
2x2−3x+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:
(x−a)(x−b)
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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