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# Determine the number and type of solution to the equation:?

Determine the number and type of solution to the equation:

8y^2 = 6y - 7

A) Exactly one real solution.

B) Exactly two real solutions.

C) Exactly two complex, but not real, solutions.

### 1 Answer

- ?Lv 71 decade agoFavorite Answer
You can find it by using determinant.

First move everything to one side and set the other side equal to 0.

-8y^2 + 6y - 7 =0

Comparing this to the standard form, ay^2 + by + c =0, we see that a = -8, b = 6, and c = -7.

Determinant D = b^2 - 4ac. Plug in the numbers to find D.

D = b^2 - 4ac = 6^2 - 4(-8)(-7) = -188

If D > 0, then you have two real different solutions.

If D = 0, then you have one real solution (double root).

If D < 0, then you have zero real solution, but two conjugate imaginary (complex) solutions.

Since our D = -188 < 0, we have two imaginary (complex) solutions.

So the correct answer is C).