a and b are roots of equation x^2-2x-2=0. what are a^2+b^2?

There are two methods to determine the sum of the square
of the roots of the given quadratic equation.

One of them
is to use Viete's relations.

We know that the sum of the
roots of the quadratic is the following:

a + b =
-(-2)/1

a + b = 2

The product
of the roots is:

a*b =
-2/1

a*b = -2

The sum of the
squares of the roots could be found using the formula:

(a +
b)^2 = a^2 + 2ab + b^2

We'll subtract 2ab both
sides:

(a + b)^2 - 2ab = a^2 +
b^2

We'll replace a + b and a*b by its
values:

(2)^2 - 2*(-2) = a^2 +
b^2

4 + 4 = a^2 + b^2

a^2 +
b^2 = 8

The sum of the squares of the roots
of the quadratic equation is a^2 + b^2 = 8.