College Math CLEP Prep Practice Exam

If the discriminant of a quadratic equation is 24, what type of solutions will the equation have?

1. Imaginary

2. Complex

3. Real and Distinct

4. Real and Equal

The correct answer is: Real and Distinct

The discriminant of a quadratic equation is the value found under the square root in the quadratic formula. It is used to determine the nature of the solutions to a quadratic equation. In this case, since the discriminant is a positive number (24), the equation will have two distinct real solutions. This means that when graphed, the parabola will intersect the x-axis at two distinct points. Option A is incorrect because having imaginary solutions means that the discriminant will be negative. Option B is also incorrect because complex solutions refer to solutions that involve both real and imaginary numbers. In this case, the solutions will only involve real numbers. Option D is incorrect because having equal solutions means that the discriminant will be equal to 0, but in this case, the discriminant is 24. Therefore, the correct answer is C Real and Distinct.