10
advanced-math

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

A

±10\pm 10

B

10 only

C

5

D

±5\pm 5

Correct Answer: A

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}.