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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Expansion and factorization to determine roots of equations

Let $(a,c)$ be the roots of the equation $x ^ 2 + ax - b = 0$. Let $(b,d)$ be the roots of the equation $x ^ 2 + cx + d = 0$. Find all the possible real values for $a, b, c, d$. NOTE: I have made very little progress towards the answer and any…
Carli
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AS Maths simplify

A question in my AS Exam this morning was simply, Simplify $(5\sqrt5)^3$ I tried $(5\sqrt5 \cdot 5\sqrt5)^2$ and ended with $5^4$. Is that correct? I think it's completely wrong, but it'd be awesome if someone could point my problem out. Thank…
user230432
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Positive Zeroes within a Polynomial

Question: Let $a,b>0.$ Can the polynomial $$x^{10} − x^7 + 2x^5 + ax^3 − bx + 1$$ have exactly three (counting multiplicity) positive zeroes? Can it have three simple positive zeroes together with one positive zero of multiplicity two? Explain. I…
Nevolute
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Root question help needed

$$\sqrt{3+\sqrt{3+\sqrt{3+x}}}=x$$ Question is: How to find x? Could you help me? Thanks in advance
Enes
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Solving for $x$, ${\sqrt{7x-5}} - {\sqrt{2x}} = {\sqrt{15 - 7x}}$

could I please have some help solving this equation for $x$ ? ${\sqrt{7x-5}} - {\sqrt{2x}} = {\sqrt{15 - 7x}}$ Thank you
PlsHelpMe
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Showing that at least one of the equations has two real roots

Let's suppose that $b_1, b_2, c_1, c_2$ are real numbers. We know that $b_1b_2=2(c_1+c_2)$. The task is to prove that at least one of the equations $x^2+b_1x+c_1=0$, $x^2+b_2x+c_2=0$ has two real roots. I tried with $b_1^2-4c_1>0$ or…
Vincent
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Find the value of $a$ from the equation

The roots of the equation: $ax^2-(5a+2)x+9a=0$ are equal. Find the value of $a$ given that $a>0$.
Harry
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Solve this equation $(2x^2-3)^2=4(x-1)^2$?

This is the way I solved: What should I do next? Should I factorize or take a t that represents something?
user219242
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Problem with the Bisection method

I have a problem by using the bisection method. I have to get a route of 2xcos(2x)-sin(2x)=0 in the interval (3,4) However by the first estimation, I got a positive number when I put f(3.5) therefore the next interval is (3,3.5). However the…
user163990
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if $a,b,c$ are the roots of $x^3-px^2+qx-r=0$, find the value of $(a+b-c)(b+c-a)(c+a-b)$

If $a,b,c$ are the roots of $ x^3-px^2+qx-r=0$, find the value of $(a+b-c)(b+c-a)(c+a-b):$ A) $p^3 -8r$ B) $4pq-p^3$ C) $4pq-p^3-8r$ D) $4pq-8r$ Solution: $$a+b+c= p$$ $$ab+bc+ca= q$$ $$abc= r$$ Using above we get: $$(p-2a)(p-2b)(p-2c)$$
rst
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root of $a-b{{e}^{cx}}-{{e}^{\left( c+d \right)x}}=0$

I am trying to find the root(s) of this equation, basically write variable x in terms of parameters a, b, c, and d. not sure how to proceed. Thanks! $$a-b{{e}^{cx}}-{{e}^{\left( c+d \right)x}}=0$$
Eln
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If square root is the inverse function of $5^2$ what is the inverse function of $5^1$

I am not great at maths or anything, but just had a general question: If square root is the opposite of $5^2$, what is the opposite of $5^1$, $5^3$, $5^4$? Is there an opposite? How would I work it out? I may be having a brain freeze but thank you…
neeko
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root of equation using bisection method

We have the equation $f(x)=x^3-7x^2 + 14x -6 $ .I have to find the root of the equation using bisection method in the interval of $]1.3 , 2 [$ First I find $f(1.3)=2.567 >0 $ and $f(2)=2>0$ I guess this means that based on the Intermediate Value…
user3543012
  • 139
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Find a solution for an equation

Is there any way to find the solution for $x$ in this equation: $$ x^2 = e^{2\mu} \left(e^{2x^2} - e^{x^2} \right) $$ Where $\mu$ has a constant value. I appreciate in advance.
ehsanM
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For each number $d$ dividing 12, list the a's with $1 \leq a < 13$ and $e_{13} (a) = d$

For each number $d$ dividing 12, list the a's with $1 \leq a < 13$ and $e_{13} (a) = d$ Can some explain the method of solving this number theory problem. Giving me a hard time, thanks.
Pasie15
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