This week in pre-calculus 11 we were introduced to the discriminant located in the square root of the quadratic formula. Using the discriminant you are given lots of information about the formula. You can evaluate if the equation is factorable or not, how many possible solutions there are and if the answer is rational, irrational, real and unreal. The way of determining how many possible is with these rules below.
- x > 0 (Then it has 2 solutions)
- x = 0 (Then it has 1 solution)
- x < 0 (Then it has no solutions)
When given the example
From the equation, we see a= 6, b = 10 and c= -1
Plugging these values into the discriminant, we get:
$latex b2−4ac $
$latex 10^2−4(6)(−1) $
= 124
This is a positive number, so the quadratic has two solutions.
This makes sense if we think about the corresponding graph.
Notice how it crosses the -axis at two points.
In other words, there are two solutions that have a -value of 0, so there must be two solutions