Find the roots of following quadratic equation $5m^2\,-\,2m\,=\,2$
- $\displaystyle\,m\,=\,\frac{1\,\pm\,\sqrt{9}}{5}$
- $\displaystyle\,m\,=\,\frac{-1\,\pm\,\sqrt{11}}{5}$
- $\displaystyle\,m\,=\,\frac{1\,\pm\,\sqrt{11}}{5}$
- $\displaystyle\,m\,=\,\frac{1\,\pm\,\sqrt{13}}{5}$
Reveal answer
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C
Correct answer
Explanation
5m^2 - 2m - 2 = 0. Using the quadratic formula m = [-b +/- sqrt(b^2 - 4ac)] / 2a. m = [2 +/- sqrt(4 - 4*5*(-2))] / 10 = [2 +/- sqrt(4 + 40)] / 10 = [2 +/- sqrt(44)] / 10 = [2 +/- 2*sqrt(11)] / 10 = [1 +/- sqrt(11)] / 5.
AI explanation
Rearranging gives 5m^2 - 2m - 2 = 0. Using the quadratic formula, the roots are m = (2 plus or minus sqrt(4 + 40)) / 10, which simplifies to m = (1 plus or minus sqrt(11)) / 5.