The Quadratic Formula
If you want to solve a quadratic equation, the quadratic formula can be used to solve for the unknown variable. For an equation of the form ax2 + bx + c = 0, where a ≠ 0.
\(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)
Example: Solve the equation 6x2 - x - 1 = 0.
Solution:
\(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)
\(=\frac{-(-1)\pm\sqrt{(-1)^2-4(6)(-1)}}{2(6)}\)
\(=\frac{1\pm\sqrt{25}}{12}\)
\(=\frac{1+5}{12}\) or \(\frac{1-5}{12}\)
\(=\frac{6}{12}\) or \(\frac{-4}{12}\)
\(=\frac{1}{2}\) or \(\frac{-1}{3}\)
Example: Solve the equation 2x2 + 3x - 4 = 0.
Solution:
\(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)
\(=\frac{-3\pm\sqrt{3^2-4(2)(-4)}}{2(2)}\)
\(=\frac{-3\pm\sqrt{41}}{4}\)
Example:
