Question

In simplest radical form, what are the solutions to the quadratic equation 0 =-3x² - 4x + 5?

Answer 1

$\bf ~~~~~~~~~~~~\textit{quadratic formula} \\\\ 0=\stackrel{\stackrel{a}{\downarrow }}{-3}x^2\stackrel{\stackrel{b}{\downarrow }}{-4}x\stackrel{\stackrel{c}{\downarrow }}{+5} \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x = \cfrac{-(-4)\pm\sqrt{(-4)^2-4(-3)(5)}}{2(-3)}\implies x = \cfrac{4\pm\sqrt{16+60}}{-6} \\\\\\ x = \cfrac{4\pm\sqrt{76}}{-6}\implies x = \cfrac{-4\mp\sqrt{4\cdot 19}}{6}\implies x = \cfrac{-4\mp\sqrt{2^2\cdot 19}}{6}$

$\bf x = \cfrac{-\stackrel{2}{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\mp ~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\sqrt{19}}{\underset{3}{~~\begin{matrix} 6 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\implies x = \cfrac{-2\mp \sqrt{19}}{3}$