3
advanced-math

Solve using the quadratic formula: x2+3x−5=0x^2 + 3x - 5 = 0

A

x=−3±292x = \frac{-3 \pm \sqrt{29}}{2}

B

x=3±292x = \frac{3 \pm \sqrt{29}}{2}

C

x=−3±112x = \frac{-3 \pm \sqrt{11}}{2}

D

x=−3±291x = \frac{-3 \pm \sqrt{29}}{1}

Correct Answer: A

Choice A is the correct answer. The quadratic formula is x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.

  1. Identify: a=1,b=3,c=−5a=1, b=3, c=-5.
  2. Discriminant: 32−4(1)(−5)=9+20=293^2 - 4(1)(-5) = 9 + 20 = 29.
  3. Substitute: x=−3±292(1)x = \frac{-3 \pm \sqrt{29}}{2(1)}.

Choice B is incorrect because it uses +b+b instead of −b-b in the numerator. Choice C is incorrect because it calculates the discriminant as 9−20=−119 - 20 = -11 (sign error). Choice D is incorrect because the denominator is 2a2a, not aa.

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