Let be a polynomial function of degree 2 and for all

MATHEMATICS · Subjective · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Let

f(x)

be a polynomial function of degree 2 and

f(x) > 0

for all

x \in \mathbb{R}

. If

g(x) = f(x) + f'(x) + f''(x)

, then for any

x

show that

g(x) > 0

.

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