16Hit1600
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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