# Tagged Questions

Linear, exponential, logarithmic, polynomial, rational, and trigonometric functions, conic sections, binomial, surds, graphs and transformations of graphs, equation- and system-solving, and other symbolic-manipulation topics.

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### Sum of the $11^\mathrm{th}$ power of the roots of the equation $x^5+5x+1=0$

Find the sum of the $11^\mathrm{th}$ power of the all roots of the equation $$x^5+5x+1=0$$ My Attempt: Let $R=\{\alpha,\beta,\gamma,\delta,\mu\}$ be the set of all roots of the equation ...
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### find gcd$( \lfloor x \rfloor, \lfloor x^a \rfloor)$

Is there a way to find gcd$( \lfloor x \rfloor, \lfloor x^a \rfloor)$ assume that $x>1$ and can assume that $a>0$. Also, if close form doesn't exist are there meaningful lower bounds and upper ...
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### Circumference of separate circle

So I have been out of Algebra for a while now. I am trying to help my wife prep for an entrance exam and we ran across this in the practice test: ...
49 views

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### Method for finding function from graphs

I have a linear line on a graph that intersects the y axis at 0.1 and the x axis at 1. Very simple, however for the life of me I can't remember the process for finding the function expression. By ...
85 views

### Is this real number an integer?

Is this real number : $$\Big(2+\frac{10}{9}\sqrt{3}\Big)^{1/3}+\Big(2-\frac{10}{9}\sqrt{3}\Big)^{1/3}$$ an integer ? I've tried different factorization, but nothing seems to work.
1k views

### Factoring a quadratic with number in front of $x^2$

I have not yet understood how to factor a quadratic that contains a number in front of $x^2$, without using the quadratic equation. I am used to just brute forcing numbers such that AB and A + B are ...
262 views

### Factorizing Cubic equation into quadratic and linear equation?

If it is given that $x^2+x+1$ is a factor of : $ax^3+bx^2+cx+d=0$ How can we write the above equation as $\left(x^2+x+1\right)\left(ax+d\right)=0$ Where did the 'b' and 'c' dissappear.
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### Why are points from this matrix geometric sequence co-planar?

Let $M= \left[ {\begin{array}{ccc} a_{1,1} & a_{1,2} & a_{1,3} \\ a_{2,1} & a_{2,2} & a_{2,3} \\ a_{3,1} & a_{3,2} & a_{3,3} \\ \end{array} } \right]$, such ...
2k views

### Where did the negative answer come from?

The question is to evaluate $\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\cdots }}}}$ $$x=\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\cdots }}}}$$ $$x^2=2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\cdots }}}}$$ $$x^2=2+x$$ ...
The question states " Simplify: $$\frac{6\left ( 27^{2n+3} \right )}{9^{3n+6}}$$ What I did was factoring $9$ and and $27$ to make it $3$. In the end I got a $\frac{6}{27}$ answer, simplified: ...