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Oscar Murray - Opin... Untitled document -.. a. x^(2)-6x+8=0

a. x2−6x+8=0 x^{2}-6 x+8=0

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Full solution

Q. a. x2−6x+8=0 x^{2}-6 x+8=0
  1. Identify coefficients: Identify the coefficients of the quadratic equation x2−6x+8=0x^2 - 6x + 8 = 0. Here, a=1a = 1, b=−6b = -6, and c=8c = 8.
  2. Use quadratic formula: Use the quadratic formula x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} to find the roots. Substitute aa, bb, and cc into the formula.
  3. Calculate discriminant: Calculate the discriminant: b2−4ac=(−6)2−4⋅1⋅8=36−32=4b^2 - 4ac = (-6)^2 - 4\cdot1\cdot8 = 36 - 32 = 4.
  4. Substitute values: Substitute the values into the quadratic formula: x=6±42⋅1=6±22x = \frac{6 \pm \sqrt{4}}{2 \cdot 1} = \frac{6 \pm 2}{2}.
  5. Solve for x: Solve for x: x=(6+2)/2=8/2=4x = (6 + 2) / 2 = 8 / 2 = 4 and x=(6−2)/2=4/2=2x = (6 - 2) / 2 = 4 / 2 = 2.

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