To determine the number of real solutions for the quadratic equation \(4x^2 - 3x + 2 = 0\) using the discriminant, we will apply the following formula for the discriminant \(D\):
\[ D = b^2 - 4ac \]
Here, the coefficients are:
- \(a = 4\)
- \(b = -3\)
- \(c = 2\)
Now, we can calculate the discriminant:
\[ D = (-3)^2 - 4(4)(2) = 9 - 32 = -23 \]
Since the discriminant \(D\) is negative (\(-23 < 0\)), this indicates that the quadratic equation has 2 complex solutions.
Therefore, the correct response is: 2 complex solutions.
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