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Solve: x^2 - 5x + 6 = 0

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Answer
x=2,x=3\boxed{x = 2, x = 3}

Substituting x=2x=2 gives 4−10+6=04 - 10 + 6 = 0, and substituting x=3x=3 gives 9−15+6=09 - 15 + 6 = 0, confirming both solutions are correct.

Problem: Solve the quadratic equation x2−5x+6=0x^2 - 5x + 6 = 0.

Steps

  1. Factor the quadratic expression
    (x−2)(x−3)=0(x - 2)(x - 3) = 0
  2. Apply the Zero Product Property
    x−2=0orx−3=0x - 2 = 0 \quad \text{or} \quad x - 3 = 0
  3. Solve for x
    x=2orx=3x = 2 \quad \text{or} \quad x = 3

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