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How many real solutions does the equatio...

How many real solutions does the equation `x^7+14 x^5+16 x^3+30 x-560=0` have?

A

1

B

3

C

5

D

7

Text Solution

Verified by Experts

The correct Answer is:
A
Let `f(x)=x^(7)+14x^(5)+16x^(3)+30x-560`
`:'f'(x)=7x^(6)+70x^(4)+48x^(2)+30gt0, AA x epsilonR`
`impliesf(x)` is an increasing function, for all `x epsilonR`
Hence number of real solution is 1.
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