Solve the quadratic equation for real roots: 2x^2 - 5x - 12 = 0.
Answer and explanation
Correct answer: B. x = 4 or x = -1.5
- Step 1: Use the quadratic formula x = [-b +- sqrt(b^2 - 4ac)] / (2a) with a=2, b=-5, c=-12.
- Step 2: Compute discriminant: b^2 - 4ac = (-5)^2 - 4(2)(-12) = 25 + 96 = 121.
- Step 3: Find roots: x = (5 +- 11) / 4. Therefore, x = 16/4 = 4 or x = -6/4 = -1.5.
Answer
x = 4 or x = -1.5.
Why not the others: Option x = -4 or x = 1.5 reverses root signs. Option x = 3 or x = -2 factors the trinomial with incorrect linear coefficients. Option x = 6 or x = -1 fails the middle term check (2*(-1) + 6 != -5).
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