Gate2017 ss Q10

0. The number of roots of ex + 0.5x2 - 2 =0 in the range [-5,5] is ______.

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