What is the discriminant of the quadratic equation 2x^2 + 5x - 3 = 0, and what does it indicate about the roots?
Answer and explanation
Correct answer: A. Discriminant = 49
- Step 1: The discriminant is Delta = b^2 - 4ac = 5^2 - 4(2)(-3) = 25 - (-24) = 49. Step 2. Since Delta = 49 > 0 and 49 is a perfect square (7^2), there are two distinct real rational roots. Answer: Discriminant = 49. Why not the others: A negative discriminant would yield complex roots, and Delta = 0 yields repeated roots.
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