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Simple
Simple
6:18 AM
why does zero consider as a polynomial but not as constant in $R[x]$
 
Martin Sleziak
Martin Sleziak
@Simple I am not really sure that this is true - is it written somewhere in this way?
However, zero polynomial is still rather special. Every $x\in R$ is a root. No other polynomial has this property. Other constant polynomials do not have any roots at all.
 
Simple
Simple
6:53 AM
it's a true or false question. the original question polynomials of $Q[x]$ without the constant term is subsapce of $Q[x]$, the answer is true. My thought it is not because it does not have zero
 
Martin Sleziak
Martin Sleziak
By "polynomials of $Q[x]$ without the constant term" they probably mean polynomials of the form $a_nx^n+\dots+a_1x+a_0$, where $a_i\in Q$ and $a_0=0$.
For example, you could say that $x^2+2x=x^2+2x+0$ "has constant term" - but it is zero.
But I will agree that the question is a bit ambiguous. (Or, at the very least, it could be formulated more clearly.)
Anyway, you will probably agree that the set of all polynomials with $a_0=0$ over some field Q forms a vector subspace of Q[x].
 
Martin Sleziak
Martin Sleziak
7:21 AM
I will certainly admit, that I would be unsure whether to answer true or false to the question phrased in this way.
 
 
1 hour later…
Math Geek
Math Geek
8:43 AM
is there any website or free software that directly converts math equations to MathJax code?
i'm a high school student and not much interested in learning in coding.i just want to ask math questions here.
please help.
Don't consider me rude.I'm interested in mathematics not computer science.
 

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