Week 7 in Precalc 11

This week in math we learned about discriminants and how to determine the nature of a root. The discriminant equation is $b^2$-4ac, as taken from the part of the quadratic formula under the root sign. There is some important vocabulary to know when determining the nature of a root. Distinct roots: two solutions, positive number, #>0. Real roots: #≥0. Equal roots: #=0. Rational roots: perfect square. Irrational roots: isn’t a perfect square. No roots/unreal roots: negative number, #<0. Remember these terms when determining the nature of a root so you can use the proper vocabulary as an answer.

Next, onto how to use the discriminant equation, $b^2$-4ac. When you are given an equation, you can use this formula by inputting the correct numbers into it. The equation you have must be in the form of a $x^2$+bx+c=0, a≠0. An important note is that although a cannot be 0, b or c can. It is possible you will have to rearrange an equation to get it in this format (equal to zero) or possibly simplify it to make it easier to work with. Let’s start off with a simple example:

3 $x^2$-18x+27=0
3( $x^2$-6x+9)=0
a= 1, b=-6, c=9 $b^2$-4ac $(-6)^2$-4(1)(9)
36-36
=0; the nature of the root is a real root, equal root, and rational root.

Look at another example below: 