. The equation $x^3 +10 x^2 − 100 x + 1729 = 0$ has at least one complex root $α$ such that $ | α | > 12$.
120457
Show that the equation, $x^3+10x^2-100x+1729=0$ has at least one complex root $z$ such that $|z|>12.$
51804
How to show that a root of the equation $x (x+1)(x+2) ....... (x+2009) = c $ can have multiplicity at most 2?
25981
Prove that $\sum_{k=0}^n a_k x^k = 0$ has at least $1$ real root if $\sum_{k=0}^n \frac{a_k}{k+1} = 0$
148983
If $a$, $b$, $c$ are the roots of $x^3-6x^2+3x+1=0$, find all possible values of $a^2b+b^2c+c^2a$
36331
One root common to $ax^2+2bx+c=0$ and $dx^2+2ex+f=0$
69288
Number of real roots of $\sum_{k=0}^{n}\frac{x^{k}}{k!}=0$
118266
If $f^2(b) - f^2(a) = b^2 - a^2$, then the equation $f'(x)f(x) = x$ has at least one root in (a, b).
20305
Complex roots of $z^3 + \bar{z} = 0$
116616
Could $X^3 + X + 1$ have a root in $E?$
61047
Find the coefficient of ${x^9}$ in the expansion of $ (1 + x)( 1 + x^2)( 1 + x^3)..(1 + x^{100})$
148243
Prove that there are no positive integers $x$ and $y$ such that $x^3 + y^3 = 10^3$.
83402
equation of a circle that has a radius of $\sqrt{10}$
141093
How many real roots does $(x-a)^3+(x-b)^3+(x-c)^3$ have?
138078
Solve $2000x^6+100x^5+10x^3+x-2=0$
47949
If $a$ and $b$ are two roots of $x^4 + x^3 - 1 = 0$ prove that $ab$ is a root of $x^6 + x^4 + x^3 - x^2 - 1$.
114542
Can a number with $100$ $0$'s $100$ $1$'s and $100$ $2$'s ever be a perfect square?
155527
Find coefficient for $x^{10}$ in $x^3(x^2-3x^3-1)^6$