Find the roots of following quadratic equation $9s^2\,-\,4\,=\,-6s $
- $\displaystyle\,s\,=\,\frac{-1\,\pm\,\sqrt5}{3}$
- $\displaystyle\,s\,=\,\frac{-1\,\pm\,\sqrt5}{2}$
- $\displaystyle\,s\,=\,\frac{-5\,\pm\,\sqrt5}{3}$
- $\displaystyle\,s\,=\,\frac{-1\,\pm\,\sqrt5}{4}$
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A
Correct answer
Explanation
9s^2 + 6s - 4 = 0. Using quadratic formula: s = (-b +/- sqrt(b^2 - 4ac)) / 2a. s = (-6 +/- sqrt(36 - 4*9*(-4))) / 18 = (-6 +/- sqrt(36 + 144)) / 18 = (-6 +/- sqrt(180)) / 18 = (-6 +/- 6*sqrt(5)) / 18 = (-1 +/- sqrt(5)) / 3.
AI explanation
Rewrite the given equation as 9s^2 + 6s - 4 = 0 to obtain the standard form where a = 9, b = 6, and c = -4. Apply the quadratic formula to get s = (-6 plus or minus the square root of (36 - 4(9)(-4))) divided by 18. Simplifying the expression under the square root gives 180, so s = (-6 plus or minus 6 times the square root of 5) divided by 18, which results in s = (-1 plus or minus the square root of 5) divided by 3.