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May 26th, 2019, 10:07 PM   #1
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Number of solutions

Given equation(with respect to x): $\displaystyle x^n +x=nx $ , how many real solutions the equation has ?
$\displaystyle x\geq 0 \; $ and $\displaystyle n\in \mathbb{N} $.
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May 27th, 2019, 01:55 AM   #2
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May 28th, 2019, 07:07 AM   #3
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By factorization of the equation : $\displaystyle n\cdot x $ is totally independent to a constant .
So the number of real solutions is 2.
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May 28th, 2019, 11:13 AM   #4
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Your reasoning is unclear. Does it always apply?
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May 29th, 2019, 12:42 AM   #5
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Quote:
Originally Posted by skipjack View Post
Your reasoning is unclear. Does it always apply?
It is enough to just factorize the polynomial and then equal the factors with 0.
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May 29th, 2019, 05:42 AM   #6
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How exactly do you proceed in that way to your conclusion?
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