Advanced MathVery hardCoefficient for exactly one real zero
Advanced Math practice question
If k > 0 and the quadratic expression x² + kx + 25 has exactly one real zero, what is the value of k?
Answer: 10
One real zero means the discriminant is zero: k² − 4(1)(25) = 0, so k² = 100 and k = 10 (taking the positive root). Then x² + 10x + 25 = (x + 5)².
Common wrong answers
- If you answered 5
- 5 is the number inside the perfect square (x + 5)²; k is twice that.
- If you answered 25
- 25 is the constant term, not k.
- If you answered 100
- 100 is k², one step short of k.
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