Substitute the values for a, b, and c into b2 – 4ac to determine the discriminant. Which quadratic equations will have two real number solutions? (The related quadratic function will have two x-intercepts.) Check all that apply. 0 = 2x2 – 7x – 90 = x2 – 4x + 40 = 4x2 – 3x – 10 = x2 – 2x – 80 = 3x2 + 5x + 3

A quadratic has two real solutions when its discriminant, b² − 4ac, is greater than zero. For A, the discriminant is (−7)² − 4(2)(−9) = 121; for C, it is (−3)² − 4(4)(−1) = 25; and for D, it is (−2)² − 4(1)(−8) = 36. Each is positive, so these equations have two real solutions. B has discriminant 0, and E has discriminant −11, so neither has two real solutions.

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