1

Set 11: Quadratic Equations (Advanced)

Explanation

Answer: A

Solve: 2x2+x−3=02x^2 + x - 3 = 0

A.

x=1,−1.5x = 1, -1.5

✓ Correct
B.

x=−1,1.5x = -1, 1.5

C.

x=1,3x = 1, 3

D.

x=−1,−3x = -1, -3

Detailed Explanation

Choice A is correct. Choice A is the correct answer. 1. Identify: a=2,b=1,c=−3a=2, b=1, c=-3. 2. Discriminant: 12−4(2)(−3)=1+24=251^2 - 4(2)(-3) = 1 + 24 = 25. 3. Formula: x=−1±252(2)=−1±54x = \frac{-1 \pm \sqrt{25}}{2(2)} = \frac{-1 \pm 5}{4}. 4. Case 1: (−1+5)/4=4/4=1(-1 + 5)/4 = 4/4 = 1. 5. Case 2: (−1−5)/4=−6/4=−1.5(-1 - 5)/4 = -6/4 = -1.5. Choice B is incorrect because of sign errors (x=−1,1.5x = -1, 1.5). Choice C is incorrect because it ignores the denominator. Choice D is incorrect because it guesses integers without solving.

Key Steps:

•

The correct answer is x=1,−1.5x = 1, -1.5

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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