Multiple choice

Find the roots of the following quadratic equation $4p^2\,+\,7\,=\,12p$

  1. $\displaystyle\,p\,=\,\frac{5\,\pm \,\sqrt2}{2}$
  2. $\displaystyle\,p\,=\,\frac{4\,\pm \,\sqrt2}{2}$
  3. $\displaystyle\,p\,=\,\frac{3\,\pm \,\sqrt2}{2}$
  4. $\displaystyle\,p\,=\,\frac{2\,\pm \,\sqrt2}{2}$
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C Correct answer
Explanation

4p^2 - 12p + 7 = 0. Using quadratic formula p = [-b +/- sqrt(b^2 - 4ac)] / 2a. p = [12 +/- sqrt(144 - 112)] / 8 = [12 +/- sqrt(32)] / 8 = [12 +/- 4*sqrt(2)] / 8 = [3 +/- sqrt(2)] / 2.

AI explanation

Rearranging gives 4p^2 - 12p + 7 = 0. Using the quadratic formula, the roots are p = (12 plus or minus sqrt(144 - 112)) / 8, which simplifies to p = (12 plus or minus sqrt(32)) / 8, or p = (3 plus or minus sqrt(2)) / 2.

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