Question

select the correct answer.
what are the solutions of the quadratic equation below?
\\( 3x^2 - x = 11 \\)
\\( \bigcirc \\) a. \\( \frac{1\pm\sqrt{133}}{6} \\)
\\( \bigcirc \\) b. \\( \frac{-1\pm\sqrt{133}}{6} \\)
\\( \bigcirc \\) c. \\( \frac{\pm\sqrt{133}}{6} \\)
\\( \bigcirc \\) d. \\( \frac{\pm\sqrt{133}}{3} \\)

Explanation:

Step1: Rewrite in standard form

$3x^2 - x - 11 = 0$

Step2: Identify a, b, c

$a=3$, $b=-1$, $c=-11$

Step3: Calculate discriminant

$\Delta = (-1)^2 - 4(3)(-11) = 1 + 132 = 133$

Step4: Apply quadratic formula

$x = \frac{-(-1)\pm\sqrt{133}}{2(3)} = \frac{1\pm\sqrt{133}}{6}$

Answer:

A. $\frac{1\pm\sqrt{133}}{6}$