Question

Please help!!!! The roots of x^2-2x-2=0 are A.1+square root of 3 B.1+square root of 12 or C.No real roots

Answer 1

Answer:

A

Step-by-step explanation:

We have the equation:

$x^2-2x-2=0$

We can use the quadratic formula. In this case, a = 1, b = -2, and c = -2. Hence:

$\displaystyle x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1)(-2)}}{2(1)}$

Evaluate:

$\displaystyle x=\frac{2\pm\sqrt{12}}{2}$

Simplify:

$\sqrt{12}=\sqrt{4}\cdot\sqrt{3}=2\sqrt{3}$

Hence:

$\displaystyle x=\frac{2\pm2\sqrt{3}}{2}$

Divide:

$x=1\pm\sqrt3$

The correct answer is A.