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
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.
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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.