Section2The Quadratic Formula
The next theorem gives us a formula for the solutions of a second-degree polynomial equation. Note how the WeBWorK problem references the theorem.
Theorem2.1Quadratic Formula
Given the second-degree polynomial equation \(ax^2 + bx + c = 0\), where \(a\neq0\), solutions are given by \[x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}.\]
\begin{align*}
ax^2 + bx + c &= 0\\
ax^2 + bx &= -c\\
4ax^2 + 4bx &= -4c\\
4ax^2 + 4bx + b^2 &= b^2 - 4ac\\
(2ax + b)^2 &= b^2 - 4ac\\
2ax + b &=\pm\sqrt{b^2 - 4ac}\\
2ax &=-b\pm\sqrt{b^2 - 4ac}\\
x &=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}
\end{align*}
Exercise 2.2 Solving Quadratic Equations
