Question

Real numbers a, b, and c are nonzero constants and b squared, minus 4 a, c, equals negative 9b2−4ac=−9 . How many real numbers x satisfy the equation a, x squared, plus b x, plus c, equals 0ax2+bx+c=0 ?

Answer 1

The given quadratic equation has no real number solutions because the discriminant is negative. Therefore, the answer is zero real number solutions.

Step-by-step explanation:

The question asks how many real numbers x satisfy the quadratic equation ax2+bx+c=0 given that the discriminant b2-4ac equals -9. The discriminant in the quadratic formula -b ± √(b2-4ac) over 2a determines the nature of the roots.

Since the discriminant is negative (specifically, -9), the quadratic equation will not have any real number solutions. A negative discriminant indicates that the equation has two complex (non-real) solutions.

Therefore, the answer to how many real numbers satisfy the given quadratic equation is zero.