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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
Put the equation in the form ax%5E2%2Bbx%2Bc=0 first.
3+%2B+8z%5E2+=+-7z
8z%5E2%2B7z%2B3=0
Now comparing coefficients to the general equation,
a=8
b=7
c=3
The formula for the discriminant is,
D=b%5E2-4ac=%287%29%5E2-4%288%29%283%29=49-96=-47
Since D%3C0, 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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+graph%28+300%2C+300%2C+-5%2C+5%2C+-5%2C+5%2C+8x%5E2%2B7x%2B3%29+
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Also, if D=0, you have 1 rational root, a double root.
If D%3E0, you have 2 distinct roots. If D is a perfect square(1,4,9,16,...), then the two roots will be rational, if not then they will be irrational.