Show that the polynomial has at least one zero in the interval $(0,1)$.
25981
Prove that $\sum_{k=0}^n a_k x^k = 0$ has at least $1$ real root if $\sum_{k=0}^n \frac{a_k}{k+1} = 0$
75002
show that $\det(A)=0$ in this case
155444
Show that entire function $f$ is a polynomial of degree at most $n$
129834
Show that there is a unique polynomial of degree at most $2n+1$ such that $q^{[k]}(x_1)=a_k,$ $q^{[k]}(x_2)=b_k$ for $k=0, \dots, n$.
80397
Show that this set of polynomials is ideal in F[x]
27540
A polynomial can not have infinite number of constant values
94682
Polynomial: prove there is no double root
135385
$0 < a_0 \leq a_1 \leq \cdots \leq a_n$, show $ p_n(z) = a_0 z^n + a_1 z^{n-1} + \cdots + a_{n-1} z + a_n = 0$ has no root in $|z| < 1$
6484
Polynomials in one variable with infinitely many roots.
49121
Factorizing a polynomial $f$ in $A[x]$ (with $A$ commutative), where $f$ has a zero in its field of fractions
156034
sufficient condition for a polynomial to have roots in $[0,1]$
76955
Proof the Legendre polynomial $P_n$ has $n$ distinct real zeros
39514
how do I prove that $1 > 0$ in an ordered field?
148813
Prove: $f: \mathbb{R} \rightarrow \mathbb{R}$ st for every $x \in \mathbb{R}$ there exists $n$ st $f^{(n)}(x) = 0$, f is a polynomial.
91000
Prove that $\frac{1}{a+1}0$
152347
Proof that a certain entire function is a polynomial
67291
Prove that there exists $n\in\mathbb{N}$ such that $f^{(n)}$ has at least n+1 zeros on $(-1,1)$