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.
- ?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).