# Tagged Questions

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### Solve in $\mathbb{R}$: $(x^2-3x-2)^2-3(x^2-3x-2)-2-x=0$

Solve in $\mathbb{R}$: $(x^2-3x-2)^2-3(x^2-3x-2)-2-x=0$ I'm supposed to solve this equation. It's from a math contest so solving it by hand would be preferable (no quartic formulas). I thought ...
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### Solve the following equation: $\frac{1}{x^2}+\frac{1}{(4-\sqrt{3}x)^2}=1$

Solve the following equation: $$\frac{1}{x^2}+\frac{1}{(4-\sqrt{3}x)^2}=1$$ I know it's from a Math Olympiad but I don't know which and I couldn't find it on the internet. Expanding everything ...
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### Roots Of Monic Cubic

I'm currently preparing for the USA Mathematical Talent Search competition. I've been brushing up my proof-writing skills for several weeks now, but one area that I have not been formally taught about ...
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### Finding all such polynomials under a gcd condition

Find all such polynomial $f(x)\in \mathbb{Z}[x]$ such that $$\forall n\in \mathbb{N} \quad \gcd(f(n),f(2^n))=1$$ This is a problem from the Indian Team Selection Test. Can someone give me a solution ...
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### Find all polynomials $P$ such that $P(x^2+1)=P(x)^2+1$

Find all polynomials $P$ such that $P(x^2+1)=P(x)^2+1$
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### Help me solve this olympiad challenge?

Given: $$p(x) = x^4 - 5773x^3 - 46464x^2 - 5773x + 46$$ What is the sum of all arctan of all the roots of $p(x)$?
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### Ordered quadruples in a grid

Moderator Note: This question is from a contest which ended on 22 Oct 2012. Consider $(\alpha_1, \alpha_2, \alpha_3, \alpha_4)$ such that the ordered quadruple satisfies the following: ...
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### What is shortcut to this contest algebra problem about polynomial?

The polynomial $P(x)=x^4 + ax^3 + bx^2 +cx + d$ has the property that $p(k)=11k$ for $k=1,2,3,4$. Compute $c$. The answer is $-39$.
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### Interscholastic Mathematics League Senior B #12

Compute the product of the nonreal roots of the equation $x^4+4x^3+6x^2+1004x+1001=0$. So here is what I have done so far. I got two of the roots to be zero and 4 since ...
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### Interscholastic Mathematic League Senior B Division #11

The roots of the equation 3x^3-38x^2+cx-192=0 form a geometric progression. Compute c.
From a St. Petersburg school olympiad, 11th grade. Prove or disprove: a non constant polynomial $P$ with non-negative integer coefficients is uniquely determined by its values $P(2)$ and $P(P(2))$.