how-many-x-R-satisfy-x-99-99x-1-0-

Question Number 153420 by alcohol last updated on 07/Sep/21

h o w m a n y x \in R s a t i s f y x^{99} - 99 x + 1 = 0

Answered by mr W last updated on 07/Sep/21

f^{'} (x) = 99 x^{98} - 99 = 0

x = \pm 1

f (- 1) = - 1 + 99 + 1 = 99

f (1) = 1 - 99 + 1 = - 97

f (- \infty) \to - \infty

f (+ \infty) \to + \infty

\Rightarrow t h r e e r e a l r o o t s!

Commented by mr W last updated on 07/Sep/21

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