roots and discriminant question?

Question

Evaluate the discriminant and select the choice that describes the nature of the roots of the equation.
x2-2x -2 =0

(a) real, rational, and unequal
(b) real, rational, and equal
(c) real, irrational, and unequal
(d) imaginary

Answer 1

The equation is:
x^2 - 2x - 2 = 0

The discriminant is:
(-2)^2 - 4*(-2) = 12

Now you can answer the question.

Answer 2

Discriminant = D = b^2-4ac = (-2)^2 -4(1)(-2) =4+8 =12

Thus the roots are real, irrational, and unequal
The roots are real because D>0
The roots are irrational because sqrt(D) is irrational
The roots are unequal because D not = 0
The roots are not imaginary because Dnot < 0