SOLUTION: Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one ration

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Question 247788: Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions.
9x2 + 4x - 5 = 0
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
9x2 + 4x - 5 = 0
see below for help on discriminant
imaginary solutions would have i sqrt(-1)
irrational would have the sqrt sign
http://en.wikipedia.org/wiki/Irrational_number
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=196 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 0.555555555555556, -1. Here's your graph:
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