Quadratic Equations

Quadratic Equations

We have already solved linear equations, equations of the form \(ax+by=c\). In linear equations, the variables have no exponents. Quadratic equations are equations in which the variable is squared. Listed below are some examples of quadratic equations:

\(\begin{array}{cccccccccc}\hfill {x}^{2}+5x+6=0\hfill & & & \hfill 3{y}^{2}+4y=10\hfill & & & \hfill 64{u}^{2}-81=0\hfill & & & \hfill n\left(n+1\right)=42\hfill \end{array}\)

The last equation doesn’t appear to have the variable squared, but when we simplify the expression on the left we will get \({n}^{2}+n\).

The general form of a quadratic equation is \(a{x}^{2}+bx+c=0,\text{with}\phantom{\rule{0.2em}{0ex}}a\ne 0\).

To solve quadratic equations we need methods different than the ones we used in solving linear equations. We will look at one method here and then several others in a later tutorial.