Question

The number of roots of e^x + 0.5x² - 2 = 0 in the range [-5,5] is 

(A) 0 

(B) 1 

(C) 2 

(D) 3

Answer 1

Correct option is (A) 0 

f(x) = e^x + 0.5x² -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].