Week 10 – Math 11

This week in math 11 we learned how to solve quadratic inequalities. This is something that we started in math 10 with the solving part but determining wether x is greater then (x >), less than (x <), or is is equal to and greater then or less than ( X \leq X \geq).

The first thing that you are going to want to do is factor out your expression and find the zeroes / roots of the expression. For example if your equation is 2x^2-8x-10\leq0 then that would factor down to 2(x+1)(x-5) meaning your roots are X=-1 and X=5.

Next you put those two numbers on a line (roughly where they would be on a number line) and determine your three test numbers. Your test numbers are numbers that are in the three sections of your line. These numbers are either greater than or less than one of your roots. For example for this questions your test numbers would be -2, 0, 10. The reason I chose those numbers is because -2 is less then -1 and is an easy number to use, 0 because when ever you can use zero you should, and 10 because is is easier then some of the numbers after 5.

Now you are going to put, one at a time, the test numbers into the equation and see if its true or false (remember that since the symbol is equal to or greater then then you would draw a coloured in dot on the line). Once you know what part of the line is true or false then you know what your positive and negative are. Since section 1 is true and section 3, then that would mean that x\leq-1 and x\geq5

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