4
advanced-math

Solve: 2x2+x−3=02x^2 + x - 3 = 0

A

x=1,−1.5x = 1, -1.5

B

x=−1,1.5x = -1, 1.5

C

x=1,3x = 1, 3

D

x=−1,−3x = -1, -3

Correct Answer: A

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.

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