Questions tagged [algebra-precalculus]
For questions about algebra and precalculus topics, which include linear, exponential, logarithmic, polynomial, rational, and trigonometric functions; conic sections, binomial, surds, graphs and transformations of graphs, solving equations and systems of equations; and other symbolic manipulation topics.
165
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Is there any simple trick that can be used to simplify this radical expression?
$$
\frac{1}{\sqrt{2} + 1} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + 2}=1
$$
I came across this on a practice standardized test. The question was to evaluate the left hand side, and it ...
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0
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34
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How do we create this linear equation?
Given two pair of equations:
Pair 1
$(.5+.5r)(.5-r)=A_0$
$(.5+.5r)^2(.5-r)=B_0$
Pair 2
$(r-.5)(1-.5r)=A_0$
$(r-.5)^2(1-.5r)=B_0$
We are given a pair of two values $A_0, B_0$ that satisfy Pair 1 or ...
0
votes
0
answers
14
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Limitation of functions in describing sequences in condensed form.
Are there boundaries till which a function or a combination of functions can explain another function? If so which branch of mathematics deals with it?
For example- The Fibonacci sequence has a ...
3
votes
2
answers
74
views
ACT practice test, aren't both $3$ and $12$ viable answers?
The question
For which of the following values of $c$ will there be two distinct real solutions to the equation $5x^2+16x+c=0$?
and the possible answers are:$\quad$
$\text{F}.\space3\\
\text{G}.\...
- 71
0
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1
answer
92
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Where does the third solution come from?
There's a well known trick with polynomials. If we have
\begin{align*}
&&(x-r_1)(x-r_2) &= 0 \\
&& x^2 -(r_1+r_2)x + r_1r_2 &=0 \tag{*}\label{*} \\
&\text{so}& x^2 &...
- 1,509
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0
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38
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I need help finding the upper and lower bounds of a polynomial's roots
I used rational root theorem to obtain the possible roots of
$f(x)=-x^4+3x^3-4x^2-7x+9$
The upper boundary I obtained from rational root theorem was $3$. When I used $3$ in synthetic division I got ...
- 11
1
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0
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37
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Degree with which a polynomial changes with some small change
Soft question: I was curious as to how one could measure the degree with which a polynomial is perturbed. More formally, let $P(x) \in \mathbb{C}$ be a polynomial and $\epsilon$ be a very small number,...
- 166
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votes
1
answer
88
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Can you cross multiply two fractions in an equation when the denominator is zero? [closed]
I just had a debate with my math teacher today. He was teaching us about straight lines. He was trying to prove some equation for which he needed to cross-multiply two fractions on two sides of an ...
- 1
1
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1
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258
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Sum of the vectors from centre $O$ to the polygon vertices
I'm attempting to calculate the sum of the vectors from the center of a regular polygon to each of the vertices. I have already solve it in a complex analysis manner:
To represent the vertices of a ...
- 23
1
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0
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31
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Any algebraic simplification for the following?
As part of a problem I'm solving with polynomials I am confronted with the expression:
$$f(x,y) = \left(\prod_{m=0, m\neq j}^na_j-a_m\right)^{-1}\left(\prod_{m=0, m\neq j}^n(x+y-a_m) - \prod_{m=0, m\...
- 166
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0
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226
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How to rationalize the denominator [closed]
help i am in 8th grade and my teacher ask this question: rationalize the denominator in $1/(1+\sqrt2)$. idk where to start
-1
votes
0
answers
41
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Quicker and non-trivial methods for solving Cubic Equation
Motivation : There have been many elementary ways like Hit-and-trial method, Polynomial division and others used in teaching how to solve cubic equation. I wanted to find a method that is faster to ...
- 95
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0
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Is there a rule for using parentheses or brackets after the summation symbol to indicate what is included in the sum? [duplicate]
Using parentheses or brackets removes ambiguity but is it necessary?
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1
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71
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How do I prove this statement about polynomials of degree greater than 1? [closed]
Consider the polynomial equation $p(x)=a$. Let $x_0$ be a solution. I want to prove that, if $p(X)$ and $a$ have the same sign for some $X\in\mathbb R$, then
$$\frac{a}{p(X)}>1\implies \frac a{p(X)}...
- 590
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0
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41
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Restrictions or lack thereof. [closed]
Help me with this problem.
Let $p$ and $q$ be real numbers. If the result of the power $p^q$ is 0, then it is always true that:
$a)p=0$
$b)q=0$
$c)p=1$
$d)q=1$
$e)p=q$
The answer they give as ...
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