Find a quadratic equation whose roots are the reciprocals of the roots of 3x^2+5x-2=0.

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