GATE 2017 CS (CS2) – Question 9

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

How many roots does $e^x+0.5x^2-2=0$ have in [−5,5]?

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Correct answer: (C) 2

Explanation

Let f(x)=eˣ+x²/2−2. Since f″(x)=eˣ+1>0, f is strictly convex and f′ is strictly increasing, allowing at most two roots. f(−5)>0, f(0)=−1 and f(5)>0, so the intermediate value theorem supplies one root on each side of zero. Exactly two, C.

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