What is the value of the discriminant, b2 − 4ac, for the quadratic equation 0 = −2x2 − 3x + 8, and what does it mean about the number of real solutions the equation has?
Answer
A
The discriminant is −55, so the equation has 2 real solutions.
B
The discriminant is −55, so the equation has no real solutions.
C
The discriminant is 73, so the equation has 2 real solutions.
D
The discriminant is 73, so the equation has no real solutions.
Explanation
For 0 = −2x² − 3x + 8, the coefficients are a = −2, b = −3, and c = 8. The discriminant is b² − 4ac = (−3)² − 4(−2)(8) = 9 + 64 = 73. Since the discriminant is positive, the equation has two real solutions, so choice C is correct.
AI-written and checked against the verified answer.