Correct option is **(A) 0 **

f(x) = e^{x} + 0.5x^{2} -2

f(-5) = 10.50; f(-4) = 6.01, f(-2) = 0.135; f (-1) = -1.13;

f(0) = -1, f(1) = 1.21, f(2) = 7.38, f (3), f(4), f (5) also + ve.

∴ As there are 2 sign changes from +ve to –ve and –ve to +ve, two roots will be there in the range [-5, 5].