Question: Find an equation whose roots are the reciprocals of the roots of 2x^2 + x -4 = 0

What i did so far:

sum = -b/a = -1/2 --> reciprocal = -2

product = c/a = -2 --> reciprocal = -1/2

Therefore, x^2 - (sum)x + (product) = x^2 - (-2)x + (-1/2)

= 2x^2 + 4x -1

From other sources, another answered showed: 4x^2 + x -2

Can someone verify whether what i did is correct?