SOLUTION: Use the discriminant to determine whether the following equations have solutions that are : 2 diff. rational solutions,2 diff. irrational solutions, exactly 1 rational solution, or

Question 311967: Use the discriminant to determine whether the following equations have solutions that are : 2 diff. rational solutions,2 diff. irrational solutions, exactly 1 rational solution, or 2 different imaginary solutions.
3 + 8z^2 = -7z
I am so confused, I just am not catching on to the quadratic equations
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Put the equation in the form first.

Now comparing coefficients to the general equation,

The formula for the discriminant is,

Since , you will have two different imaginary roots.
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Graphically, the curve never touches the x-axis, there are no real solutions.
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Also, if , you have 1 rational root, a double root.
If , you have 2 distinct roots. If is a perfect square(1,4,9,16,...), then the two roots will be rational, if not then they will be irrational.
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