CMA Foundation · Fundamentals of Business Mathematics and Statistics · Quadratic Equations
For the equation 2x^2 - 8x + k = 0, the roots are real and equal. What is the value of k?
The value of k is 8. Real and equal roots require the discriminant to be zero, so 64 - 8k = 0, giving k = 8. The equation then becomes 2(x - 2)^2 = 0 with a repeated root x = 2.
- A4
- B16
- C8Correct
- D-8
Explanation
Equal roots require discriminant b^2 - 4ac = 0. Here 64 - 4(2)(k) = 0, so 8k = 64 and k = 8. Check: 2x^2 - 8x + 8 = 2(x-2)^2. Option 16 comes from forgetting the coefficient a=2 (64-4k=0).
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