Multiple choice

Find the roots of the quadratic equation by applying the quadratic formula $\displaystyle 2x^2 - 7x + 3 = 0$

  1. $3,\displaystyle -\frac{1}{2}$
  2. $-3,\displaystyle \frac{1}{2}$
  3. $3,\displaystyle \frac{1}{2}$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the quadratic formula x = [-b +/- sqrt(b^2 - 4ac)] / 2a. For 2x^2 - 7x + 3 = 0, x = [7 +/- sqrt(49 - 24)] / 4 = [7 +/- 5] / 4. Roots are 12/4 = 3 and 2/4 = 1/2.

AI explanation

Applying the quadratic formula to 2x^2 - 7x + 3 = 0, we first calculate the discriminant as D = (-7)^2 - 4(2)(3), which equals 49 - 24 = 25. The roots are given by x = (7 +/- sqrt(25)) / 4, resulting in x = (7 + 5) / 4 = 3 and x = (7 - 5) / 4 = 1/2. The roots of the equation are 3 and 1/2.

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