Answer:
[tex] x_{1} = 3 + \sqrt {6} [/tex]
[tex] x_{2} = 3 - \sqrt {6} [/tex]
Step-by-step explanation:
Given the quadratic equation;
x² - 6x + 3 = 0
To find the roots of the quadratic equation, we would use the quadratic formula;
Note: the standard form of a quadratic equation is ax² + bx + c = 0
a = 1, b = -6 and c = 3
The quadratic equation formula is;
[tex] x = \frac {-b \; \pm \sqrt {b^{2} - 4ac}}{2a} [/tex]
Substituting into the formula, we have;
[tex] x = \frac {-(-6) \; \pm \sqrt {-6^{2} - 4*1*(3)}}{2*1} [/tex]
[tex] x = \frac {6 \pm \sqrt {36 - (12)}}{2} [/tex]
[tex] x = \frac {6 \pm \sqrt {36 - 12}}{2} [/tex]
[tex] x = \frac {6 \pm \sqrt {24}}{2} [/tex]
[tex] x = \frac {6 \pm 2 \sqrt {6}}{2} [/tex]
[tex] x_{1} = \frac {6 + 2 \sqrt {6}}{2} [/tex]
[tex] x_{1} = \frac {6}{2} + \frac {2 \sqrt {6}}{2} [/tex]
[tex] x_{1} = 3 + \sqrt {6} [/tex]
Or
[tex] x_{2} = \frac {6 - 2 \sqrt {6}}{2} [/tex]
[tex] x_{2} = \frac {6}{2} - \frac {2 \sqrt {6}}{2} [/tex]
[tex] x_{2} = 3 - \sqrt {6} [/tex]
