SOLUTION: CAN SOMEONE PLEASE HELP ME WITH THIS PROBLEM: Use the discriminant to determine the number of real solutions of the equation. 7 + 5z^2 = 2z

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Question 161257: CAN SOMEONE PLEASE HELP ME WITH THIS PROBLEM:
Use the discriminant to determine the number of real solutions of the equation.
7 + 5z^2 = 2z
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The discriminant for a quadratic equation is given by
b%5E2-4ac when the equation is in the form
ax%5E2%2Bbx%2Bc=0
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7+%2B+5z%5E2+=+2z
Rearrange the equation,
5z%5E2-2z%2B7=0
In your case,
a=5
b=-2
c=7
The discriminant is then,
b%5E2-4ac=%28-2%29%5E2-4%285%29%287%29
b%5E2-4ac=4-144
b%5E2-4ac=-148
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The discriminant gives you information regarding the roots depending on its value.
If b%5E2-4ac%3E0, you have two distinct real roots.
If b%5E2-4ac=0, you have two coincident real roots.
If b%5E2-4ac%3C0, you have two complex roots (complex conjugates).
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Since b%5E2-4ac=-148, you will have two complex conjugate roots.