Multiple choice

Find the roots of each of the following quadratic equations by the method of completing the squares $2x^2 - 5x + 3 = 0$

  1. $x=2,\,\,x=-7$
  2. $x=-1,\,\,x=3$
  3. $x=\displaystyle 1,x= \frac{3}{2}$
  4. $x=\displaystyle 1, x=\frac{1}{2}$
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C Correct answer
Explanation

2x^2 - 5x + 3 = 0. Divide by 2: x^2 - 2.5x + 1.5 = 0. (x - 1.25)^2 - 1.5625 + 1.5 = 0. (x - 1.25)^2 = 0.0625. x - 1.25 = +/- 0.25. x = 1.5 or x = 1.

AI explanation

To solve 2x squared minus 5x plus 3 equals 0 by completing the square, we divide by 2 and rearrange to get x squared minus 2.5x equals negative 1.5. Adding the square of half the x coefficient, which is 1.25 squared or 1.5625, to both sides forms x squared minus 2.5x plus 1.5625 equals 0.0625. This perfect square factors to (x minus 1.25) squared equals 0.0625, so taking the square root of both sides yields x minus 1.25 equals 0.25 or negative 0.25. Solving these two equations results in the roots x equals 1 and x equals 1.5, which is three halves.

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