query: $ f(x) = 3^x+4^x-5^x$ has only one root
positive_passages.docid: 63505
positive_passages.text: Proving that $ 2 $ is the only real solution of $ 3^x+4^x=5^x $
negative_passages.docid: 40212
negative_passages.text: roots of $f(z)=z^4+8z^3+3z^2+8z+3=0$ in the right half plane
negative_passages.docid: 30511
negative_passages.text: Monic $f(x)\in\Bbb Z[x]$ has no rational root if $f(0)\ \&\ f(1)$ odd [Parity Root Test, Modular Root Test]
negative_passages.docid: 2300
negative_passages.text: Determine the remainder when $f(x) = 3x^5 - 5x^2 + 4x + 1$ is divided by $(x-1)(x+2)$
negative_passages.docid: 56877
negative_passages.text: Show that $\sqrt{4 + 2\sqrt{3}} - \sqrt{3}$ is rational.
negative_passages.docid: 122407
negative_passages.text: If $f(x) = x^3+3x+4\;,$ Then value of $ \int_{-1}^{1}f(x)dx+\int_{0}^{4}f^{-1}(x)dx$
negative_passages.docid: 31768
negative_passages.text: Roots of a functionwith condition $\int_0^\pi f(x) \sin x dx = \int_0^\pi f(x) \cos x dx =0.$
negative_passages.docid: 152841
negative_passages.text: I want to show that $f(x)=x.f(1)$ where $f:R\to R$ is additive.
negative_passages.docid: 82567
negative_passages.text: Prove that $ f(x) $ has at least two real roots in $ (0,\pi) $
negative_passages.docid: 55248
negative_passages.text: Positive integral solutions of $3^x+4^y=5^z$
negative_passages.docid: 4178
negative_passages.text: Solve $f(x)f(2x^2) = f(2x^3+x)$
negative_passages.docid: 85383
negative_passages.text: No. Of real roots of an equation
negative_passages.docid: 135774
negative_passages.text: Alternating roots of $f(x) = \exp(x) \sin(x) -1$ and $\exp(x)\cos(x) +1$
negative_passages.docid: 121076
negative_passages.text: Show $x^p-t$ has no root in the field $\mathbb{F}_p(t)$
negative_passages.docid: 94682
negative_passages.text: Polynomial: prove there is no double root
negative_passages.docid: 18336
negative_passages.text: $x^p-c$ has no root in a field $F$ if and only if $x^p-c$ is irreducible?
negative_passages.docid: 87735
negative_passages.text: Prove that the roots $\in \Bbb R$ of $x^3+x+1=0$ aren't rational without RRT