Week 6 in Precalc 11

This week in math we learned how to solve quadratic equations using the zero product law. A quadratic equation is one that has two answers. A linear equation has one answer and a cubic equation has three. The zero product law is that if two numbers that are multiplied by each other equal zero, then one of those numbers must be zero. Using this law we can solve quadratic equations.

Say you are given an equation, for example: $x^2$-5x-14=0. The first step in solving this is to factor the equation, so $x^2$-5x-14 in factored version is (x+2)(x-7)=0. Since we know the equation is equal to zero, we can find what x is. So x+2=0 and x-7=0. These equations are very simple and easy to solve. So, x=-2 or x=7. This is the answer to the equation.

There are variations of this format that you can still solve. For example, if there is a coefficient in front of the factored version of the equation, e.g. 5x(x+2)(x-7)=0, you do the same thing for the leading number as you would for those in the brackets, so 5x=0, x=0. Then when you find the other two answers, this equation is cubic. Sometimes the answer behind the equal sign will not be 0, so you’ll have to simplify the equation so everything is on one side of the equation and then factor it. Keep in mind simple factoring laws (C- common difference, D- difference of squares, P- pattern, E- easy, U- ugly) when you are factoring the equation, these laws are very important to know and understand. I’ve included an example below of a quadratic equation solved.