Calculate the discriminant for the equation:
\[ x^2 + 2x - 2 = 0 \]
Answer (2)
x 2 + 2 x − 2 = 0 a = 1 , b = 2 , c = − 2 Δ = b 2 − 4 a c = 2 2 − 4 ∗ 1 ∗ ( − 2 ) = 4 + 8 = 12 Δ = \1 12 = 4 ∗ 3 = 2 3 x 1 = 2 a − b − Δ = 2 − 2 − 2 3 = 2 2 ( − 1 − 3 ) = − 1 − 3 x 2 = 2 a − b + Δ = 2 − 2 + 2 3 = 2 2 ( − 1 + 3 ) = − 1 + 3
The discriminant for the equation x 2 + 2 x − 2 = 0 is 12 . This positive discriminant indicates that the equation has two distinct real roots. Thus, we can conclude that the quadratic equation's solutions will be real and different from each other.
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