1. Show that the discriminant A(f) = [(x - x) (x2 x3)(x3 X)] -...

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1. Show that the discriminant A(f) = [(x₁ - x₂) (x2 − x3)(x3 — X₁)]² - of f = X³ +pX+q is equal to A(f) = (4p³ + 27q²) 1, 2, 3 are the roots of f. 2. suppose p, q are real numbers. Prove that the equation f(X) = X³ +pX + q = 0 has 3 different roots if and only if A(f) > 0. 1. Show that the discriminant A(f) = [(x₁ - x₂) (x2 − x3)(x3 — X₁)]² - of f = X³ +pX+q is equal to A(f) = (4p³ + 27q²) 1, 2, 3 are the roots of f. 2. suppose p, q are real numbers. Prove that the equation f(X) = X³ +pX + q = 0 has 3 different roots if and only if A(f) > 0.

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1 First expand the discriminant of f x1 x2 x2 x3 x3 x1 Using the fact that T1 T2 T3 ... View the full answer