CMA Foundation · Fundamentals of Business Mathematics and Statistics · Quadratic Equations
For the quadratic equation 2x^2 - 5x + 3 = 0, the discriminant and the nature of its roots are:
The discriminant is 25 minus 24, which equals 1. A positive perfect square discriminant means the roots are real, rational and unequal. Here the roots are 3/2 and 1, confirming the result.
- A1; real, rational and unequalCorrect
- B-1; imaginary
- C49; real, rational and unequal
- D0; real and equal
Explanation
Discriminant D = b^2 - 4ac = 25 - 4(2)(3) = 25 - 24 = 1. Since D is positive and a perfect square, the roots are real, rational and unequal (x = 3/2 and 1). The value 49 comes from wrongly adding 4ac instead of subtracting it.
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