Answer to Question #94125 in Physics for Roaia

Question

The value of uhich make x=2 is one of the roots of the equation X^2-2ax+2(a^2-6)=0 is

Answer 1

$f(x) = x^2-2ax+2(a^2-6)=0; \\ x = 2: f(2) = 0; \\ 2^2 - 2\cdot a \cdot2 + 2(a^2-6) = 0; \\ 2 - 2a + a^2-6 = 0; \\ a^2 - 2a -4 = 0; \\ a_{1,2} = \frac{2 \pm \sqrt{2^2 + 4\cdot1\cdot4}}{2} = \frac{2 \pm \sqrt{20}}{2} = 1 \pm \sqrt{5}.$