Question

Please help!! Use the quadratic formula to solve the equation 3x^2-x+6=0 x=

Answer 1

$\bf ~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{3}x^2\stackrel{\stackrel{b}{\downarrow }}{-1}x\stackrel{\stackrel{c}{\downarrow }}{+6} \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x=\cfrac{ - (-1) \pm \sqrt { (-1)^2 -4(3)(6)}}{2(3)}\implies x=\cfrac{1\pm\sqrt{1-72}}{6} \\\\\\ x=\cfrac{1\pm\sqrt{-71}}{6}\implies x=\cfrac{1\pm i\sqrt{71}}{6}\implies x= \begin{cases} \cfrac{1+ i\sqrt{71}}{6}\\[1em] \cfrac{1- i\sqrt{71}}{6} \end{cases}$