The Zero Factor Property: If $ab=0$, then either $a=0$ or $b=0$.
Example: Solve the equation $(2x-3)(x+5)=0$
Example: Solve the equation $x^2-3x+2=0$
Examples
$56r^2-82r+30=0$
$12u^2=32u+35$
Using Graphs to Solve Quadratic Equations
Example: Use the graph of $y=−x^2+3x+4$ below to solve the equation $−x^2+3x+4=0.$
Constructing Equations with Given Roots
Example: Construct a quadratic equation having roots $x=-2$ and $x=3$
Example: Construct a quadratic equation with the following solutions: $\gamma=-\frac{17}{2}$ or $\gamma=-\frac{11}{7}$.
Application Involving Area
Example: The base of the triangle shown in the figure is 10 cm longer than the height. Determine the height of the triangle if its area is 48 cm2.