CMA Foundation · Fundamentals of Business Mathematics and Statistics · Quadratic Equations
The equation 2x² + 5x − 3 = 0 is given. What is the nature of its roots, and what is the value of its discriminant?
The discriminant is 49, so the roots are real, rational and unequal. Since D = 5² − 4(2)(−3) = 49 is a positive perfect square, the roots are rational; indeed they are 1/2 and −3.
- AReal, rational and unequal; discriminant 49Correct
- BReal, irrational and unequal; discriminant 49
- CReal and equal; discriminant 0
- DImaginary; discriminant −24
Explanation
D = 25 − 4(2)(−3) = 25 + 24 = 49, which is a positive perfect square, so roots are real, rational and unequal. Check: (2x − 1)(x + 3) = 0 gives x = 1/2 and −3. Option B ignores that 49 is a perfect square.
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