Prove that the odd polynomial equation $p(x)=0$ has at least one real solution (use intermediate value theorem)
13981
Proof that every polynomial of odd degree has one real root
50133
The sum of odd powered real numbers equals zero implies the numbers are inverses
68617
Show that an entire function that is real only on the real axis has at most one zero, without the argument principle
91482
Is there a short proof for the Intermediate Value Theorem
69618
What is the sum of non-real roots of the polynomial equation?
151729
Existence of a unique polynomial
33099
If $f$ is an entire function where every power series expansion has at least one 0 term, show it is a polynomial
126445
Proving the second root of a quadratic equation
91003
Prove that equation has exactly 2 solutions
51019
Polynomial problem with two conditions
2408
Show that a polynomial has at least one positive solution/root.
127056
How to prove that a polynomial of degree $n$ has at most $n$ roots?
63689
proving roots of equation $x^2+x+4f=0$ are real.
7199
Suppose that $P(x)$ is a polynomial of degree $n$ such that $P(k)=\dfrac{k}{k+1}$ for $k=0,1,\ldots,n$. Find the value of $P(n+1)$
95594
Prove that a polynomial is irreducible or the field contains a $p$th root
25981
Prove that $\sum_{k=0}^n a_k x^k = 0$ has at least $1$ real root if $\sum_{k=0}^n \frac{a_k}{k+1} = 0$
135768
Find $P(n+1)$ for a polynomial P