# Tagged Questions

243 views

### Understanding non-solvable algebraic numbers

Background We know from Galois theory that the zeros of a polynomial with rational coefficients whose Galois group is solvable can be expressed in a formula that involves rational powers of the ...
308 views

### The Conjugate Roots Theorem for Irrational Roots

The Conjugate Roots Theorem for Irrational Roots states that for a polynomial $f(x)$ with integer coefficients, if a root of the equation $f(x) = 0$ is expressed as $a+\alpha$, where $a\in\mathbb{Q}$ ...
128 views

### Third degree polynomial with integer coefficient and three irrational roots

There are some polynomial with the above characteristic, and real roots of such polynomials cannot be found using rational number theorem and irrational conjugate theorem. The example of such function ...
68 views

### Number of irrational roots of the equation $(x-1)(x-2)(3x-2)(3x+1)=21$?

The number of irrational roots of the equation $(x-1)(x-2)(3x-2)(3x+1)=21$ is (A)0 (B)2 (C)3 (d)4 Actually im a 10 class student i don't know any of it,but my elder brother(IIT Coaching) cannot ...
268 views

### Proof $\sqrt{1 + \sqrt[3]{2}}$ is irrational using the theorem about rational roots of a polynomial

I'm having trouble with this specific problem at the moment. The theorem states that if $n/m$ is a rational root of a polynomial with integer coefficients, the leading coefficient is divisible by m ...
### Is it assumable that $2^{1/12}$ is irrational because $2^{1/2}$ is?
I need to prove that $2^{1/12}$ is irrational but I need to connect this to $2^{1/2}$ being irrational. I know how to prove that $2^{1/2}$ is irrational, but can I assume that $2^{1/12}$ is irrational ...