Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [roots]

Questions about the set of values at which a given function evaluates to zero. For questions about "square roots", "cube roots" and such, consider using the (radicals) and the (arithmetic) tag. For questions about roots of Lie algebras, use the (lie-algebra) tag instead.

Questions regarding values $x$, such that a function $f$ evaluates to zero at $x$. For questions about "square roots", "cube roots" and such, consider using the and the tag. For questions about roots of Lie algebras, use the tag instead.

6663 questions
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Zeros of $ \frac{1}{B(xi)^{1/2}}((iA)^{ix})(ix)^{ix}+ \frac{1}{B(-xi)^{1/2}}((-iA)^{-ix})(-ix)^{-ix}=H(x)$

What would be the zeros of the following function? $$ \frac{1}{B(xi)^{1/2}}((iA)^{ix})(ix)^{ix}+ \frac{1}{B(-xi)^{1/2}}((-iA)^{-ix})(-ix)^{-ix}=H(x)$$ This function is real and I believe it is equal to the cosine of a certain function $$…
Jose Garcia
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Question on surds rule

Through the textbook, I've been taught the rule $\frac{\sqrt a}{\sqrt b} = \sqrt\frac{a}{b}$, however I realized that if all numbers are assumed to be real, and $a<0 ,b<0$, then the rule is not true as $\frac{\sqrt{-a}}{\sqrt{-b}} =…
nabu1227
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What will be the difference of the roots of this given equation?

What will be the difference of the roots of the equation $$ (x^2 - 10x - 29)^{-1} + (x^2 - 10x - 45)^{-1} = 2(x^2 - 10x - 69)^{-1} $$ I actually tried to solve it but it was too lengthy to calculate with the simple method I know. I want to solve it…
Resorcinol
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Understanding quadratic root

Quadratic root is defined as $\sqrt{ x^2} = |x|$. Easy to remember, but seems to lack logic. And this topic is about you proving me wrong. 1) This definition of a square root is not universal and is restricted to one special case when $x \in R$. 2)…
user3600124
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When does $f(x)/f'(x)$ have a first-order root?

Actually let $g(x)=0$ when $f(x)=0$ otherwise $g(x)=f(x)/f'(x)$. Seems clear to me that if $x_0$ is an $n$-order root of $f(x)$ where $n$ is a positive integer, and $f(x)$ can be expressed as a Taylor series about $x_0$, then $x_0$ is a first-order…
Ted Ersek
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Roots of $x^4 -6x^3 +x^2+10x +1=0$

How can one prove that the following function has 4 real roots? $$x^4 -6x^3 +x^2 +10x+1=0$$ The problem is that roots don't seem to be possible to compute by hand.
GorillaApe
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Using Vieta's Formulas to find expression involving polynomial roots

I'm having trouble with this problem. Show that if the roots of $$5x^3-x^2-2x+3=0$$ are $a_1,a_2,a_3$, then $$1/a_1+1/a_2+1/a_3=2/3$$
user183782
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Number of irrational roots of the equation $3^x8^{\frac{x}{x+1}}=36$

Find the number of irrational solutions of the equation $$3^x8^{\frac{x}{x+1}}=36.$$
udaiveer
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Finding product of roots of equation of unknown degree when a root is given

If $7^{\frac13} + 7^{\frac23}$ is a root of equation of minimum possible degree with rational coefficients, then what is the product of roots of this equation? How do I solve it?
Shaurya Gupta
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Roots of product of two functions

I wonder if the answer to this question is true: Having two functions $f(x)$, $g(x)$ where $f(x)$ has $N$ real roots, and $g(x)$ is positive for all $x$ (no real roots), does the product of $f(x)g(x)$ also have exactly $N$ roots? For example. Let…
pisoir
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Cube root equations

I am interested in finding a general method of solving equations involving cube roots such as $$x^{1/3} + (x-16)^{1/3} = (x-8)^{1/3}.$$ I have a solution for this particular one: $$\{8 - (12 \cdot 21^{1/2})/7, \quad 8 + (12 \cdot 21^{1/2})/7, \quad…
user132599
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How to determine root multiplicity from ONLY the graph?

If you were given the graph of a function, without the function's equation, is there a way to determine exact multiplicity (not just parity) of the roots of the function?
M0RF3US
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Finding the zeros of a polynomial equation.

Find the exact solutions of $x^3 + 5x^2 -2x -15 =0$. While making notes for my students (in high school), I came across this problem. Using the Rational Root Theorem there don't seem to be any rational roots that work. Is it possible to have 3 real…
user128534
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If $a$ and $b$ are the roots of $z^2 - 2z + 4 = 0$ then what is $a^n + b^n + ab$ ($n$ is a natural number)?

I don't know how to solve this question, any help would be appreciate it. If $z^2 - 2z + 4 = 0$, then what is the result of this $a^n + b^n + ab$ ($n$ is a natural number, $a$ and $b$ are the roots of that equation)?
bossModus
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Roots of the equation?

If $p,q,r$ are real numbers satisfying the condition $p + q + r =0$, then the roots of the quadratic equation $3px^2 +5qx +7r=0$ are (A)Positive (B)Negative (C)Real and distinct (d)Imaginary Actually im a 10 class student i don't know any of it, but…
user88232
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