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:
$$\int_0^1 \frac{2}{2x^2+3x+1} \,dx$$
Now, the issue I have is with factoring the demoninator.
When I used the quadratic formula:
$$\begin{equation*} x = \frac{-b \pm \sqrt{b^{2} -4ac}}{2a} \end{equation*}$$
I came up with the roots:
$$\biggl(x-\frac{1}{2}\biggl)\biggl(x-1\biggl)$$
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: $$2x^2-3x+1$$
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
HINT: it is $$2x^2+3x+1=(x+1)(2x+1)$$