CMA Foundation · Fundamentals of Business Mathematics and Statistics · Quadratic Equations
For the quadratic equation 2x² − 7x + 6 = 0, what is the value of the discriminant and what does it say about the roots?
The discriminant is 49 − 48 = 1. Since it is positive and a perfect square, the roots are real, rational and unequal, being 2 and 3/2. Using a plus sign for the 4ac term would wrongly give 97 and irrational roots.
- A1; roots are real, rational and unequalCorrect
- B1; roots are real and equal
- C−1; roots are imaginary
- D97; roots are real and irrational
Explanation
Discriminant D = b² − 4ac = 49 − 4(2)(6) = 49 − 48 = 1. D is positive and a perfect square, so the roots are real, rational and unequal (indeed x = 2 and x = 3/2). Treating D as 49 + 48 = 97 comes from a sign error on the product term.
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