# Tagged Questions

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### If two polynomials both of n degree have n identical real roots, are they equal? Proof?

CORRECTION: The polynomials don't have to be equal, but one has to be a constant multiple of the other. I ask the question because I saw this fact used in this solution to a problem: Problem: Given ...
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### Coefficients of a polynomial also are the roots of the polynomial?

How many real solutions $(r_1, r_2, \cdots, r_n)$ are there such that $(r_1, r_2, \cdots, r_n)$ are the roots of the polynomials $x^{n} + r_1 x^{n-1} + r_2 x^{n-2} + \cdots + r_n$ For $n = 2, 3, 4$ I ...
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### A 3rd degree polynomial $P(x)$ has three unequal real roots. What is the least possible # of unequal real roots for $P(x^2)$

I got that if P(x) is a 3rd degree polynomial then P($x^2$) must be a 6th degree polynomial. I don't know how to proceed from here.
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### Find the solution of the equation

Find all real solutions of this equation : $$x=\sqrt{2+\sqrt{2-\sqrt{2+x}}}$$
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### Polynomial With Imaginary Roots

Working on question 1 here http://www.sosmath.com/cyberexam/precalc/EA2002/EA2002.html Find a polynomial with integer coefficients that has the following zeros: ...
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### Can $x^3+3x^2+1=0$ be solved using high school methods?

I encountered the following problem in a high-school math text, which I wasn't able to solve using factorization/factor theorem: Solve $x^3+3x^2+1=0$ Am I missing something here, or is indeed a more ...
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### Finding the solutions of $\cos (x) +x = a$

What is the approach to finding the solutions of the following function? I was not able to analytically resolve the solutions - but rather resorted to a graphical approach. $$\cos (x) + x = 1$$ or in ...
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### How many values of c in the equation $x^2 - 5x + c$ result in rational roots which are integers?

This question was asked in the e-litmus exam.
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### Is my simple (in my opinion) way of solving cubic equations correct?

I've been analyzing ways of solving cubic equations and I've come up with this one. I've tried to make it as simple as possible. So I'll show you a way of solving cubic equations when none of the ...
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### Find all real zeros of $f(x)=2x^3+10x^2+5x-12$

Hey guys I'm having a little trouble with one problem: Find all real zeros of $$f(x)=2x^3+10x^2+5x-12.$$ I got $x=-4,(2x^2+2x-3)$. I'm just having trouble using the quadratic formula to get ...
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### Is there a known algorithm for approximating all the real and imaginary zeros of any well behaved equation of a single variable?

Does there currently exist a general algorithm (or set of algorithms used together) that will approximate all the zeros of any well behaved non-differential equation of a single variable which has a ...
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### Why doesn't $1/x=0$ have any solution?

Just out for curiosity ! Why $1/x=0$ doesn't have any solution? Or is it that the solution takes you to $1=0$ situation which would nullify mathematical principle that we stood for years Educate ...
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### Number of real roots ,eh!! [closed]

Consider $P(x)=1+x+\frac {x^2}{2}+\frac {x^3}{6}+\frac {x^4}{24}$ Find the number of real zeros of the polynomial $P(x)$
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### Solve $\left(x^{2010}+1\right)\left(1+x^2+x^4+x^6+…+x^{2008}\right)=2010x^{2009}$

Solve for $x$ $\left(x^{2010}+1\right)\left(1+x^2+x^4+x^6+.......+x^{2008}\right)=2010x^{2009}$ solution should be by hand
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### Solve $\lfloor{x}\rfloor$+$\lfloor2x\rfloor+\lfloor4x\rfloor+\lfloor16x\rfloor+\lfloor32x\rfloor=12345$

Solve for $x$ $$\lfloor{x}\rfloor+\lfloor2x\rfloor+\lfloor4x\rfloor+\lfloor16x\rfloor+\lfloor32x\rfloor=12345$$ I tried to put $x$=$I$+$f$ where $I$ is integer part and $f$ is fractional part but that ...
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### Find number of solutions of $2^x$+$3^x$+$4^x$=$5^x$

Find number of solutions of $$2^x+3^x+4^x=5^x$$ I tried using graphs but don't know how to draw graph of L.H.S.
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### Comment upon nature of the roots

How many roots are there of the following polynomial? How many are real, and how many are complex? ...
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### Polynomials - Solutions

How I can find the exact solutions of this polynomial? I can not get to the exact roots of the polynomial ... what methods occupy for this "problem"? $$x^3+3x^2-7x+1=0$$ Thanks for your help.
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### Product and Sum of Polynomial Roots

The ratio of the sum of the roots of the equation, $8x^3+px^2-2x+1=0$ to the product of the roots of the equation $5x^3+7x^3-3x+q=0$ is $3:2$. What is the value $\frac{p-q}{p+q}$? Well I found out ...
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### Solving $\sqrt{7x-4}-\sqrt{7x-5}=\sqrt{4x-1}-\sqrt{4x-2}$

Where do I start to solve a equation for x like the one below? $$\sqrt{7x-4}-\sqrt{7x-5}=\sqrt{4x-1}-\sqrt{4x-2}$$ After squaring it, it's too complicated; but there's nothing to factor or to ...
### How to solve a polynomial with power fractions like $a-ax+x^{0.8}-x^{0.2}=0$
I have something like $a-ax+x^{0.8}-x^{0.2}=0$ with parameter a>0 and variable x>0. I know by trial and error that the equation has three real roots for parameter a greater than certain value, ...