CMA Foundation · Fundamentals of Business Mathematics and Statistics · Quadratic Equations
For which value of k does the equation x² + kx + 16 = 0 have equal real roots, given that k is positive?
The value of k is 8. Equal roots require the discriminant k² − 4ac to be zero, so k² − 64 = 0 and k = 8 for positive k. The equation then becomes (x + 4)² = 0, with a repeated root of −4.
- A4
- B16
- C6
- D8Correct
Explanation
Equal roots need discriminant zero: k² − 4(1)(16) = 0, so k² = 64 and k = 8 (positive). Check: x² + 8x + 16 = (x+4)². The value 4 would come from forgetting the factor 4 in 4ac and taking k² = 16.
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