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A very stupid question:

If a homogeneous polynomial $P(x_1,\cdots,x_k)=0$ for all $x \in \mathbb{R}^k$ then does that mean it is the zero polynomial? (I have proven this using induction but I suspect this is something rather trivial and perhaps comes from fundamental theorem).

Canine360
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    I think the best way to show this is by induction, certainly the way you proceeded. – Suzet Jun 06 '18 at 03:28
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    Yes. Prove by induction on $k$. – Angina Seng Jun 06 '18 at 03:28
  • Thank you both for your help. Is this a well-known existing result and if yes where can I find a citation (I looked for it but couldn't find it)? I actually need to use this somewhere, and I've proven it but I'd just use the citation if it's already there. Thanks so much again. – Canine360 Jun 07 '18 at 01:09

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