The equation $3x^2-2\sqrt{6}x+2=0$ has repeated factors after factoris…

Question

The equation $3x^2-2\sqrt{6}x+2=0$ has repeated factors after factorisation. What are its roots?

Accepted Answer

C. $\sqrt{\frac{2}{3}}$ and $\sqrt{\frac{2}{3}}$

We write $3x^2-2\sqrt{6}x+2=(\sqrt{3}x-\sqrt{2})(\sqrt{3}x-\sqrt{2})=(\sqrt{3}x-\sqrt{2})^2$. Thus the same linear factor occurs twice. Solving $\sqrt{3}x-\sqrt{2}=0$ gives $x=\sqrt{\frac{2}{3}}$, so both roots are equal to $\sqrt{\frac{2}{3}}$.

Answer

$\sqrt{\frac{2}{3}}$ and $-\sqrt{\frac{2}{3}}$

Answer

$\sqrt{\frac{3}{2}}$ and $\sqrt{\frac{3}{2}}$

Answer

$-\sqrt{\frac{2}{3}}$ and $-\sqrt{\frac{2}{3}}$