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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

Please Help The Roots Of X22x20 Are A1square Root Of 3 B1square Root Of 12 Or CNo Real Roots class=

Sagot :

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Answer:

A

Step-by-step explanation:

We have the equation:

[tex]x^2-2x-2=0[/tex]

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

[tex]\displaystyle x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1)(-2)}}{2(1)}[/tex]

Evaluate:

[tex]\displaystyle x=\frac{2\pm\sqrt{12}}{2}[/tex]

Simplify:

[tex]\sqrt{12}=\sqrt{4}\cdot\sqrt{3}=2\sqrt{3}[/tex]

Hence:

[tex]\displaystyle x=\frac{2\pm2\sqrt{3}}{2}[/tex]

Divide:

[tex]x=1\pm\sqrt3[/tex]

The correct answer is A.

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