4 normals can be drawn from any point to an ellipse proof doubt: How do we know the key quartic has 4 distinct real roots?
97548
Number of normals from a point to an ellipse
99999
A question on identifying normal subgroups of $S_4$
125702
There is a square $Q$ consisting of $(0,0), (2,0), (0,2), (2,2)$
63689
proving roots of equation $x^2+x+4f=0$ are real.
43300
The degree of $\sqrt{2} + \sqrt[3]{5}$ over $\mathbb Q$
17051
Determine the fourth roots of -16
13909
How to find the roots of $x^4 +1$
85869
Four complex numbers $z_1,z_2,z_3,z_4$ lie on a generalized circle if and only if they have a real cross ratio $[z_1,z_2,z_3,z_4]\in\mathbb{R}$
41193
Number of integral roots of a polynomial
2705
How many roots have modulus less than $1$?
18702
If $ax^2+(c+b)x+e+d=0$ has real roots greater than $1$, show that $ax^4+bx^3+cx^2+dx+e$ has at least one real root
62058
How to prove $1$,$\sqrt{2},\sqrt{3}$ and $\sqrt{6}$ are linearly independent over $\mathbb{Q}$?
103501
Question about a normal equation proof
154393
Roots of polynomial with real coefficients appear in conjugate pairs.
143259
Find the condition on $a$ and $b$ so that the two tangents drawn to the parabola $y^2=4ax$ from a point are normals to the parabola $x^2=4by$
63679
Picture/intuitive proof of $\cos(3 \theta) = 4 \cos^3(\theta)-3\cos(\theta)$?
141093
How many real roots does $(x-a)^3+(x-b)^3+(x-c)^3$ have?