Math miscellaneousEasy
Question
How many real solutions does the equation x7 + 14x55+ 16x3 + 30x - 560 = 0 have?
Options
A.7
B.1
C.3
D.5
Solution
x7 + 14x5 + 16x3 + 30x - 560 = 0
Let f(x) = x7 + 14x5 + 16x3 + 30x
⇒ f′(x) = 7x6 + 70x4 + 48x2 + 30 > 0 ∀ x
∴ f(x) is an increasing function ∀ x.
Let f(x) = x7 + 14x5 + 16x3 + 30x
⇒ f′(x) = 7x6 + 70x4 + 48x2 + 30 > 0 ∀ x
∴ f(x) is an increasing function ∀ x.
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