Answer:
[tex]x = \frac{4±2 \sqrt{11}i }{5} [/tex]
Step-by-step explanation:
To find the roots, we first need to figure out which formula is the best to use. We can do this by simplifying the equation first.
10x^2 - 16x + 24 = 0
(10x^2 - 16x + 24) / 2 = 0 / 2
5x^2 - 8x + 12 = 0
Since we can't factorize this resulting equation, we have to use the Quadratic Formula.
[tex]x = \frac{ -b ± \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
[tex]x = \frac{ - ( - 8)± \sqrt{( - 8)^{2} - 4(5)(12)} } {2(5)} [/tex]
[tex]x = \frac{ 8± \sqrt{64 - 240} } {10} [/tex]
[tex]x = \frac{8±4 \sqrt{11} i}{10} [/tex]
[tex]x = \frac{4±2 \sqrt{11}i }{5} [/tex]
Hope this helps!
#CarryOnLearning
