Multiple choice

Find the roots of the following quadratic equations, if they exist, by the method of completing the square. $\displaystyle 2x^2 - 7x + 3 = 0$

  1. The roots of the given quadratic equation are $\displaystyle \frac{1}{3}$ and $1$.
  2. The roots of the given quadratic equation are $\displaystyle \frac{2}{5}$ and $5$.
  3. The roots of the given quadratic equation are $\displaystyle \frac{1}{2}$ and $3$.
  4. The roots of the given quadratic equation are $\displaystyle \frac{2}{7}$ and $4$.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

2x^2 - 7x + 3 = 0. Divide by 2: x^2 - 3.5x + 1.5 = 0. (x - 1.75)^2 = 1.75^2 - 1.5 = 3.0625 - 1.5 = 1.5625. x - 1.75 = +/- 1.25. x = 3 or x = 0.5.

AI explanation

To solve 2x squared minus 7x plus 3 equals 0 by completing the square, we divide by 2 and rearrange to get x squared minus 3.5x equals negative 1.5. Adding the square of half the x coefficient, which is 1.75 squared or 3.0625, to both sides forms x squared minus 3.5x plus 3.0625 equals 1.5625. This perfect square factors to (x minus 1.75) squared equals 1.5625, so taking the square root of both sides yields x minus 1.75 equals 1.5 or negative 1.5. Solving these two equations results in the roots x equals 3 and x equals 0.5.

Keep practicing — related questions