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

Question 263330: 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.
10 - 5a2 = 7a + 9

Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
-5a^2-7a+1=0

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=69 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: -1.53066238629181, 0.130662386291807. Here's your graph:

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