To find the zeros of the quadratic polynomial p(x) = 2x² + 5x – 3, we solve the equation 2x² + 5x – 3 = 0 using the quadratic formula: x = [– b ± √(b² – 4ac)] / (2a), where a = 2, b = 5, c = – 3.

First, calculate the discriminant: D = b² – 4ac = 5² – 4(2)(– 3) = 25 + 24 = 49.1

Now, solve for x: x = [– 5 ± √49] / (2*2) = [– 5 ± 7] / 4.

This gives two solutions: x = (– 5 + 7)/4 = 2/4 = 1/2 and x = (– 5 – 7)/4 = – 12/4 = – 3.

Therefore, the zeros are 1/2 and – 3.

Final Answer: $\frac{1}{2},-3$