Final answer:
The discriminant of the quadratic equation −4x^2 + 3x −28 = 0 is negative (−439), which means there are 0 real number solutions to the equation.
Step-by-step explanation:
To determine how many real number solutions exist for the quadratic equation −4x2 + 3x −28 = 0, you can use the discriminant, which is the part of the quadratic formula under the square root sign. The discriminant is given by the formula Δ = b2 − 4ac. For the quadratic equation in question, the coefficients are a = -4, b = 3, and c = -28.
Calculating the discriminant:
Δ = (3)2 − (4)(-4)(-28)
Δ = 9 − 448
Δ = −439
Since Δ is less than 0, the quadratic equation has 0 real number solutions.
The correct answer is Option A: 0 real number solutions.