Tagged Questions
-1
votes
2answers
90 views
$\mathbb{R} \setminus \mathbb{Q}$:'a stamping tool' [closed]
What does it mean for the polynomial
$$ a_1x_1+\cdots+a_nx_n=b $$
to have solutions in $\mathbb{R} \setminus \mathbb{Q}$, where $a_i,b\in \mathbb{Q}$?
2
votes
0answers
51 views
Two quartic polynomials to be made a square?
Given two generally non-square quartic polynomials that are to be simultaneously made squares for particular values of $x$,
$$c_1x^4+c_2x^3+c_3x^2+c_4x+c_5 = y_1^2$$
...
10
votes
1answer
189 views
Why is $x^3-5x$ injective on the rationals?
I've found the statement on the internet that the polynomial $x^3-5x$ is injective on the rational numbers, but without any comments on how to prove it. I think it means it must be easy, but I don't ...
2
votes
2answers
63 views
for what value of $a$ has equation rational roots?
Suppose that we have following quadratic equation containing some constant $a$
$$ax^2-(1-2a)x+a-2=0.$$
We have to find all integers $a$,for which this equation has rational roots.
First I have ...
2
votes
1answer
102 views
Is there a rational univariat polynomial of degree 3 with 3 irrational roots?
The title pretty much asks my question: Does $f\in\mathbb{Q}[x]$ such that
$$ f(x)=(x-\alpha_1)(x-\alpha_2)(x-\alpha_3),$$
where $\alpha_1, \alpha_2, \alpha_3\in\mathbb{R}\setminus\mathbb{Q}\ $ ...
