GATE 2017 EE (EE2) – Question 9

General Aptitude · Quantitative Aptitude: Data Interpretation, Arithmetic and Number Computation · 2 marks · Multiple choice

The number of roots of $e^x+0.5x^2-2=0$ in [−5,5] is

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Correct answer: (C) 2

Explanation

Let f(x)=e^x+x²/2−2. Its second derivative is e^x+1>0, so f is strictly convex and its first derivative is strictly increasing. It can have at most two roots.

Now f(−5)>0, f(0)=−1<0 and f(5)>0. Continuity guarantees one root on each side of zero. Together with the upper bound, this proves there are **exactly two roots, C**.

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