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
The discriminant for that equation is [ B² - 4 A C ].
Thats 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.
\( the\ discriminant\ of\ the\ quadratic\ ax^2+bx+c=0\\\\\Delta=b^2-4\cdot a\cdot c\\-\\\\ x^2 + 2x -2 =0\\\\\Delta=2^2-4\cdot1\cdot(-2)=4+8=12\\\\discriminant=12 \)