Question

Find all complex solutions of 7x^2-7x+3=0

Answer 1

The complex solutions are

`x = ((7-√(35) i )/(42) , ) x = (7 + √(35) i )/(42))`

Explanation:

Step(i):-

Given equation 7 x² - 7 x +3=0

`x = (\frac{-b -\sqrt{b^(2)-4ac } }{2ac} , \frac{-b +\sqrt{b^(2)-4ac } }{2ac})`

Given standard equation

a x² +b x +c =0

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

Step(ii):-

`x = (\frac{-(-7) -\sqrt{(-7)^(2)-4(7)(3) } }{2(7)(3)} , \frac{-(-7) +\sqrt{(-7)^(2)-4(7)(3) } }{2(7)(3)})`

`x = ((7-√((49-84 ) )/(42) , (7 +√((49-84 ) )/(42))`

`x = (\frac{7-\sqrt{35i^(2) } }{42} , \frac{7 + \sqrt{35i^(2) } }{42})`

`x = ((7-√(35) i )/(42) , (7 + √(35) i )/(42))`