Question

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

Answer 1

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