GATE | GATE-CS-2017 (Set 2) | Question 6



The numbers of the roots of ex + 0.5x2 -2 = 0 in the range [-5, 5] are
(A) 0
(B) 1
(C) 2
(D) 3


Answer: (C)

Explanation: The given function is a continuous function in range [-5, 5].

The Intermediate Value Theorem states if a continuous function has values of opposite sign inside an interval, then it has a root in that interval.

The function changes sign twice in range [-5, 5].

  1. It becomes positive to negative in range [-5, 0] when ex + 0.5x2 becomes less than 2.
  2. It becomes positive to negative in range [0, 5] when ex + 0.5x2 becomes more than 2.


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