Show that the following equation has exactly $n$ real roots.
106011
Proving it has all real roots
20705
On equations $m^2+1=5^n$
118368
number of real solution of logarithmic and exponential equation
68275
Primitive Root Theorem Proof
79925
Infinitely many values of $x$ that satisfy the equations
94682
Polynomial: prove there is no double root
27494
$P_n(x):=1+ \sum_{m=1}^n\dfrac{x^m}{m!}$ has no real root for even $n$ and exactly one real root for odd $n$
96592
Showing that the roots of a polynomial with descending positive coefficients lie in the unit disc.
90612
Show that $9+9x+3x^3+6x^4+3x^5+x^6$ is irreducible given one of its roots
153816
Real Roots and Differentiation
43940
Showing that $n$ is pseudoprime to the base $a$
17082
Number of real roots of $2 \cos\left(\frac{x^2+x}{6}\right)=2^x+2^{-x}$
55210
Prove that the equation: $c_0+c_1x+\ldots+c_nx^n=0$ has a real solution between 0 and 1.
44020
Probability of $x^2+bx+c=0$ having real roots
69618
What is the sum of non-real roots of the polynomial equation?
82085
Without solving the equation, show that all nine roots of $(𝑧 − 1)^{10} = 𝑧^{10}$ lie on the line $Re (𝑧) = \frac{1}{2}$
134736
Prove using Rolle's Theorem that an equation has exactly one real solution.