The solutions for the quadratic equation 9x² - 6x + 5 = 0 are A. 2 complex roots
To determine the the type of roots the quadratic equation 9x² - 6x + 5 = 0, we use the quadratic formula to find the roots.
So, for a quadratic equation ax + bx + c = 0, the roots are
[tex]x = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}[/tex]
With a = 9, b = -6 and c = 5, the roots of our equation are
[tex]x = \frac{-(-6) +/- \sqrt{(-6)^{2} - 4 X 9 X 5} }{2 X 9} \\x = \frac{6 +/- \sqrt{36 - 180} }{18} \\x = \frac{6 +/- \sqrt{-144} }{18} \\x = \frac{6 +/- \sqrt{-12} }{18}\\x = \frac{6}{18} +/- i\frac{12}{18} \\x = \frac{1}{3} +/- i\frac{2}{3} \\x = \frac{1 + 2i}{3} or \frac{1 - 2i}{3}[/tex]
Since the roots of the equation are (1 + 2i)/3 and (1 - 2i)/3, there are 2 complex roots.
So, the solutions for the quadratic equation 9x² - 6x + 5 = 0 are A. 2 complex roots
Learn more about quadratic equations here:
https://brainly.com/question/18117039
