Answer:
Step-by-step explanation:
-10x² + 12x - 9 = 0
Multiply the whole equation by (-1)
10x² - 12x + 9 = 0
a = 10 ; b = -12 ; c = 9
D = b² - 4ac = (-12)² - 4*10*9
= 144 - 360
= -216
√D = √-216 = [tex]\sqrt{2*2 * 3 * 3 * 2 *3 * i^{2}}[/tex]
[tex]= 2*3*i*\sqrt{3*2}\\\\= 6i \sqrt{6}[/tex]
Roots = [tex]\frac{-b + \sqrt{D}}{2a} ; \frac{-b-\sqrt{D}}{2a}[/tex]
[tex]= \dfrac{-[-12]+6i\sqrt{6}}{2*10} \ ; \ \dfrac{-[-12] - 6i\sqrt{6}}{2*10}\\\\= \dfrac{12+6i\sqrt{6}}{20} ; \ \dfrac{12-6i\sqrt{6}}{20}\\\\\\= \dfrac{2*(6+3i\sqrt{6}}{20} ; \ \dfrac{2*(6-3i\sqrt{6}}{20}\\\\=\dfrac{6+3i\sqrt{6}}{10} ; \dfrac{6-3i\sqrt{6}}{10}[/tex]
