Refresher - Quadratic Formula

Refresher

A quadratic equation is a polynomial equation of the second degree. The general form is $a x^{2} + b x + c = 0$

where x represents a variable or an unknown, and a, b, and c are constants with $a \neq 0$ . (If a = 0, the equation is a linear equation.)

The constants a, b, and c are called respectively, the quadratic coefficient, the linear coefficient and the constant term or free term. Quadratic equations can be solved by factoring, completing the square, graphing, Newton's method, and using the quadratic formula

Quadratic formula

A quadratic equation with real or complex coefficients has two solutions, called roots. These two solutions may or may not be distinct, and they may or may not be real.

The roots are given by the quadratic formula

$LaTeX: x=\frac{-b\pm \sqrt{b^{2}-4ac } }{2a}$ $x=\frac{-b\pm \sqrt{b^{2}-4ac } }{2a}$

where the symbol ± indicates that both

$LaTeX: x=\frac{-b+ \sqrt{b^{2}-4ac } }{2a}$ $x=\frac{-b+ \sqrt{b^{2}-4ac } }{2a}$

and

$LaTeX: x=\frac{-b- \sqrt{b^{2}-4ac } }{2a}$ $x=\frac{-b- \sqrt{b^{2}-4ac } }{2a}$

are solutions of the quadratic equation.

Be careful with the signs of the values a, b and c. Don't drop the sign when substituting into the formula.

Math 1A/1B: Pre-Calculus by Dr. Sarah Eichorn and Dr. Rachel Lehman is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License Links to an external site..