query: Roots of $f(x)=3^x+4^x-5^x$
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: 130439
negative_passages.text: Finding square roots of $\sqrt 3 +3i$
negative_passages.docid: 153043
negative_passages.text: Show that $\sqrt{4+2\sqrt{3}}-\sqrt{3}$ is rational using the rational zeros theorem
negative_passages.docid: 38662
negative_passages.text: If $a,b$ are the roots of the equation $2 x^2 -3 x +1 = 0$, find an equation whose roots are $a/(2b +3)$, $b/(2a +3)$
negative_passages.docid: 59160
negative_passages.text: Roots of a given equation
negative_passages.docid: 147837
negative_passages.text: Find the parameter values satisfying conditions for all roots of an equation
negative_passages.docid: 61148
negative_passages.text: Finding real roots of $ P(x)=x^8 - x^7 +x^2 -x +15$
negative_passages.docid: 155245
negative_passages.text: root of an odd degree polynomial
negative_passages.docid: 21155
negative_passages.text: Finding basis of $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5})$ over $\mathbb{Q}$
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: 38160
negative_passages.text: Number of roots of $z^4+z^3+4z^2+2z+3=0$ in each quadrants
negative_passages.docid: 20305
negative_passages.text: Complex roots of $z^3 + \bar{z} = 0$
negative_passages.docid: 69682
negative_passages.text: Roots of $y=x^3+x^2-6x-7$
negative_passages.docid: 141184
negative_passages.text: Proof that a degree 4 polynomial has at least two roots
negative_passages.docid: 137048
negative_passages.text: If $p, q, r$ are the roots of $x^3 -x+1=0$, what is $p^5 + q^5 + r^5$?
negative_passages.docid: 122686
negative_passages.text: Find the root of the polynomial?
negative_passages.docid: 103803
negative_passages.text: Prove from first princibles $\frac{x^2-4}{x-4} \rightarrow -5$ as $x \rightarrow 3$