Final answer:
The discriminant of the polynomial 32x² + 12x - 57 is positive, indicating that the equation has two real and distinct solutions. Therefore, the statement that the polynomial has two non-real numbers is false.
Step-by-step explanation:
The question asks whether the polynomial 32x² + 12x - 57 has two non-real numbers as its solutions. To determine this, we must look at the discriminant b² - 4ac from the quadratic equation ax² + bx + c = 0. In this case, a = 32, b = 12, and c = -57.
Calculating the discriminant:
Discriminant (D) = (12)² - 4(32)(-57) = 144 + 7296 = 7440.
Since the discriminant is positive, it means that there are two real and distinct solutions for the polynomial equation. Hence, the statement about the polynomial having two non-real numbers is false.
In summary, a positive discriminant indicates real solutions, a discriminant of zero indicates one real solution (a repeated root), and a negative discriminant would be associated with non-real or complex solutions. Therefore, the answer to the question is B. False, since the discriminant of the given polynomial is positive, indicating real solutions.