Determine the roots of the quadratic equation 2x^2 - 7x + 3 = 0 using factoring.

Answer and explanation

Correct answer: D. x = 3 and x = 1/2

  1. Step 1: Find factors of ac = 23 = 6 that sum to b = -7: -6 and -1.
  2. Step 2: Rewrite: 2x^2 - 6x - x + 3 = 0.
  3. Step 3: Factor by grouping: 2x(x - 3) - 1(x - 3) = (2x - 1)(x - 3) = 0.
  4. Step 4: Set each factor to zero: 2x - 1 = 0 gives x = 1/2; x - 3 = 0 gives x = 3.
Answer
x = 3 and x = 1/2.
Why not the others: 'x = -3 and x = -1/2' makes a sign error in factoring; 'x = 2 and x = 3/2' factors incorrectly; 'x = 1 and x = 6' uses factors of 6 without dividing by leading coefficient 2.

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