Question

Can you show us how to find the discriminant of the quadratic x^2 + 2x -2 =0

Answer 1

$the\ discriminant\ of\ the\ quadratic\ ax^2+bx+c=0\\\\\Delta=b^2-4\cdot a\cdot c\\-------------------------\\\\ x^2 + 2x -2 =0\\\\\Delta=2^2-4\cdot1\cdot(-2)=4+8=12\\\\discriminant=12$

Answer 2

Step #1:
Make sure the equation is in the form of [ Ax² + Bx + C = 0 ].

Yours is already in that form.
A = 1
B = 2
C = -2

Step #2:
The 'discriminant' for that equation is [ B² - 4 A C ].
That's all there is to it, but it can tell you a lot about the roots of the equation.

-- If the discriminant is zero, then the left  side of the equation is a perfect square,
and both roots are equal. 

-- If the discriminant is greater than zero, the the roots are real and not equal.

-- If the discriminant is less than zero, then the roots are complex numbers.

The discriminant of your equation is  [ B² - 4 A C ] = 2² - 4(1)(-2) = 4 + 8 = 12

Your equation has two real, unequal roots.