Question

-

Find all complex solutions of 3x -3x+7=0.
+=.
(If there is more than one solution, separate them with commas.)
= 1
0/0
i 0,0,...
Х
?

Answer 1

Explanation:

3x² - 3x + 7 = 0

a = 3 ; b = -3 and c = 7

D = b² - 4ac = (-3)² - 4*3*7

D = 9 - 84 = - 75

D = 75i²

√D = √75i² =
`√(5*5*3 * i * i)= 5i√(3)`

`x = (-b+√(D))/(2a) \ ; \ x=(-b-√(D))/(2a)\\\\ \\x=(3+5i√(3))/(6) ; \ ; x = (3-5i√(3))/(6)\\\\\\x =(3)/(6)+(5i√(3))/(6) ; \ ; x=(3)/(6)-(5i√(3))/(6)\\\\\\Solution:\\\\x=(1)/(2)+(5√(3))/(6)i ; \ ; x=(1)/(2)-(5√(3))/(6)i`