Can you show us how to find the discriminant of the quadratic equation [tex]x^2 + 2x - 2 = 0[/tex]?

***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.

Answered by AL2006 | 2024-06-10

t h e d i scr iminan t o f t h e q u a d r a t i c a x 2 + b x + c = 0 Δ = b 2 − 4 ⋅ a ⋅ c − − − − − − − − − − − − − − − − − − − − − − − − − x 2 + 2 x − 2 = 0 Δ = 2 2 − 4 ⋅ 1 ⋅ ( − 2 ) = 4 + 8 = 12 d i scr iminan t = 12

Answered by kate200468 | 2024-06-10

To find the discriminant of the equation x 2 + 2 x − 2 = 0 , identify the coefficients A, B, and C as 1, 2, and -2, respectively. Use the formula D = B 2 − 4 A C to find that the discriminant is 12, indicating that there are two distinct real roots. Therefore, the quadratic equation has two real, unequal solutions.
;

Answered by AL2006 | 2024-12-26