Question

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

Answer 1

Answer:

The complex solutions are

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

Step-by-step 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):-

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

$x = (\frac{7-\sqrt{(49-84 } }{42} , \frac{7 +\sqrt{(49-84 } }{42})$

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

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