3x^2 + 5x - 2 = 0 3x^2 + 6x - x - 2 = 0 (3x^2 + 6x) + (-x - 2) = 0 3x(x + 2) - 1(x + 2) = 0 (3x - 1)(x + 2) = 0 3x - 1 = 0 or x + 2 = 0 3x = 1 or x = -2 x = 1/3 or x = -2
Reciprocals are 3 and -1/2 Equation with roots at 3 and -1/2 is (x - 3)(x + 1/2) = x^2 - 5/2 x - 3/2 = 2x^2 - 5x - 3 Therefore, required equation is y = 2x^2 - 5x - 3
