Question

Find the number of real roots of x^15 + 5x^5 – 3

Answer 1

hi friends the all India

Answer 2

Answer:

order by

votes

Up vote

7

Down vote

Hint. Note that f′(x)=5(x4−1)=5(x2+1)(x−1)(x+1) which implies that f is strictly increasing in (−∞,−1], it is strictly decreasing in [−1,1] and it is strictly increasing in [1,+∞). Knowing that limx→±∞f(x)=±∞, f(−1)=6, and f(1)=−2, what may we conclude