Question

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

Quadratic formula: x= -b/b2 - 4ac
20
•x= - 24/19
• x = -2 2 / 19
• x= 24/19
• x = 2:219

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√((-4)^2-4(-3)(5))}{2(-3)}\implies x = \cfrac{4\pm√(16+60)}{-6} \\\\\\ x = \cfrac{4\pm√(76)}{-6}\implies x = \cfrac{-4\mp√(4\cdot 19)}{6}\implies x = \cfrac{-4\mp√(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}~~√(19)}{\underset{3}{~~\begin{matrix} 6 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\implies x = \cfrac{-2\mp √(19)}{3}`