Multiple choice

Solve the quadratic equation $9{x^2} - 15x + 6 = 0$ by the method of completing the square.

  1. $x=-1$ and $x=\dfrac{2}{3}$
  2. $x=1$ and $x=\dfrac{1}{3}$
  3. $x=1$ and $x=\dfrac{2}{3}$

  4. None of these
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C Correct answer
AI explanation

Divide the equation 9x^2 - 15x + 6 = 0 by 3 to get 3x^2 - 5x + 2 = 0. Using the method of completing the square, add and subtract 25/12 to factor the left side into 3(x - 5/6)^2 - 1/12 = 0. Moving the constant gives (x - 5/6)^2 = 1/36, so taking the square root of both sides results in x - 5/6 = 1/6 or x - 5/6 = -1/6. Solving these yields x = 1 and x = 2/3.

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