10

Set 14: Quadratic Equations

Explanation

Answer: A

Find the value of bb such that x2+bx+25=0x^2 + bx + 25 = 0 has exactly one solution.

A.

±10\pm 10

✓ Correct
B.

10 only

C.

5

D.

±5\pm 5

Detailed Explanation

Choice A is correct. Choice A is the correct answer. For one solution, Δ=0\Delta = 0. 1. b24(1)(25)=0b^2 - 4(1)(25) = 0. 2. b2100=0b^2 - 100 = 0. 3. b2=100b^2 = 100. 4. b=±10b = \pm 10. Choice B is incorrect because it misses the negative case. Choice C is incorrect because it uses 25\sqrt{25}. Choice D is incorrect because it uses 25\sqrt{25}.

Key Steps:

The correct answer is ±10\pm 10

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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