# Tagged Questions

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### I need help proving a statement about rational roots

I have no idea where to start...this is the statement: If a polynomial of degree not greater than 5 with rational coefficients has multiple roots, it has also a rational root, except in the case ...
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### solving the inequalty

are there any ways to solve :$x^4 -6x^3 +28x^2 -64x +96 >0$ ?
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### complex roots calulation question

How can we find the roots of an equation such as:$z^2 +z +1=0 ,z \in \mathbb{C}$ ?
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### Descartes rule of signs extension

Let $V(\text{sequence})$ be the number of sign changes in the sequence, e.g. $V(-3,0,-2,9,0,1)=1$. Show that $V(a_0,a_1,...,a_n)\ge V(a_0,a_0+a_1,a_0+a_1+a_2,...)$. Furthermore, prove that if ...
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### Complex conjugate root theorem question

From the Complex conjugate root theorem we get that if a polynomial in one varaible with real coefficients has as solution $a + bi$ , than $a-bi$ must also be a solution...however, what happens if ...
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### Graphing polynomials

Sketch a graph of the polynomial $P(x)=(x-2)^2(x+1)^3$. You must plot and label the x and y intercepts and these should be the only points you plot. How do I sketch the graph of a polynomial?
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### how to solve this question of polynomials

Given the polynmial is exactly divided by $x+1$, when it is divided by $3x-1$, the remainder is $4$. The polynomial leaves remainder $hx+k$ when divided by $3x^2+2x-1$. Find $h$ and $k$. This ...
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### how to find the remainder when a polynomial $p(x)$ is divided my another polynomial $q(x)$

i was solving the question from the book IIT FOUNDATION AND OLYMPIAD - X and i was solving the problems of polynomials-III. so ...
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### Roots of $x^2 +2x +2$ Over $\mathbb{C}$

Find the roots of $x^2 +2x +2$ over $\mathbb{C}$ I need to prove somehow that the roots will be $(1 + i) , (1 - i)$ Any ideas how can I find those roots in a simple way?
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### help interpreting an abstract algebra test question

This is a take-home test problem, and I don't want help solving it, just understanding what it's asking. I've asked my prof a couple times, but she's either unwilling or unable to give me a straight ...
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### Primitive Root in Quotient Ring

Find a primitive root of $R[x]/\langle x^4+x+2 \rangle$ where $R$ is the integers mod $3$. Is there a good general stratagy to this sort of thing?
### Galois group of the quintic polynomial $X^5+X+1$
I'm trying to find the Galois group of the polynomial $p(X)= X^5+X+1$ over $\mathbb Q$. First, one notes that, if $\omega$ is a primitive cubic root of unity, then it is a root of $p(X)$. So, ...