3

Set 13: Quadratic Equations (Intermediate)

Explanation

Answer: A

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

A.

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

✓ Correct
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}

Detailed Explanation

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

Key Steps:

•

The correct answer is x=−3±292x = \frac{-3 \pm \sqrt{29}}{2}

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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