Задача Задача №3592701
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2X^2+3X-5>0
Solve the inequality 2x^2 + 3x - 5 > 0.
Factor or solve for zeros of the corresponding equation 2x^2 + 3x - 5 = 0. Discriminant: D = 3^2 - 4·2·(-5) = 9 + 40 = 49, roots: x = (-3 ± 7) / (2·2) = (-3 ± 7) / 4 → x = -5/2 and x = 1. Factorization: 2x^2 + 3x - 5 = (2x + 5)(x - 1).
Since the leading coefficient is positive, the parabola opens upward, so 2x^2 + 3x - 5 > 0 for x < -5/2 or x > 1.
Solution: (-∞, -5/2) ∪ (1, ∞).
