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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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Integer solutions of an inequality

Find the number of integer solutions less than $5$ that satisfy the inequality $$(x^ 3 + 4x 2 )(x^ 2 − 3x − 2) ≤ (x^ 3 + 4x 2 )(2x^ 2 − 6).$$ Factoring $$(x^2)(x+4)^2(x-1)$$ possible integers are $(-4,0,1,2,3,4)$ but $6$ is not in the choices,…
SuperMage1
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Finding if roots is integer

How to solve this: Is $(1782^{12}+1841^{12})^{1/12}$ an integer? Should I reexpress $1841$ in terms of $1782$, as such: $1782 = x$, and $1841 = x+59$? I can't make any progress. Please help.
DarkRunner
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Finding equivalence between the algorithmic and trigonometrical solution

For solving the complex equation $x^3$ = 1-i, approached through two ways: (i)Trigonometric solution: $x^3$ = $\sqrt(2)(\cos(\dfrac{-\pi}{4}) + i\sin(\dfrac{-\pi}{4}))$ In the generalized form, with $2k\pi$ as the interval for repetition of the…
jiten
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How to find the roots of the following equation:

How to find the roots of the following equation: $10.9-11.4 x^2+0.5 *\ln (17 x)=0 \ $ using computer program or else . I need the roots only but I have no idea to find the roots. Can anyone help me with roots of the above equation .
MAS
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In Case of Oscillation Sequence of Newtonian Method

I am learning the basic concept of Newtonian method and text book introduces a function which newtonian step values are Oscillating as a example which is Newtonian method is inapplicable. However, I think for any kind of differentiable function at…
Beverlie
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Square root of x

How many values of $$\sqrt x$$ is possible. Is it 2 or 1?The graph says only one but why not 2 one is positive an the other is negative. Please explain why is it so? But Thanks in anticipation.
Chandramauli Chakraborty
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Probability of $x^2+bx+c=0$ having real roots

Consider the quadratic equation $x^2+bx+c=0$, where $b$ and $c$ are $Uni∼[0,1]$. Let $p(b)$ represent the probability that the given equation has a real solution for a fixed value of$ b$. What is $p(1/2)$? What is the probability that$…
onelessproblem
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I need to know what is the coefficient?

I'm solving a exercise and I can't figure out something that I need to know to solve it... I need to know what is the coefficient of ∜x. I would appreciate some help. Thank you!
Sarah Jones
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how to find the zero in terms of an unknown constant in the following expression

The expression I would like to find the zero of is: $$ -407\,x^{2} + 220275\,x - 6118.75\,ax - 15296.875\,a^{2} + 1101375\,a - 19824750 $$ I would like to express the zero in terms of $a$, I have tried doing it myself but been getting stuck. I am…
Son Jerm
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Find the value of k if the roots of an equation differ by 2.

I need some help, Im trying to solve the below but to no avail, would appreciate your guidance :) Find the value of $k$ if the roots of $$3x^2+5x-k=0,$$ differ by two.
user2509708
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Kelly Criterion threshold

Say we have, $00$ $(1+xb)^q(1-x)^{1-q}=1$ $01$? Note that the latter condition guarantees exactly one solution, and without it there may be no solution. This comes up in the analysis of…
Omri
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A little help in this equation please.

The equation goes like : $$2^n = 3n.$$ There are many graphing calculators using which we can solve it but how can we solve it manually without a calculator?
Nippun Sharma
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Help to put Expression equal to zero

I have this expression $$g = \sqrt {2\ln {{{\sigma ^2}} \over {{{2r} \over {\sqrt a }}x\log x{e^{ - a{{(r + (1/2){\sigma ^2})}^2}\tau /(2{\sigma ^2})}}}}}.$$ I want to put this expression equal to zero so it would be something like $$0 =…
user10699
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Real cubed roots of r

If r is any real-number, then r has a real cube root, which is $\sqrt[3]{r}$. Show that $w$$\sqrt[3]{r}$ and $w^2$$\sqrt[3]{r}$ are also cube roots. Not really sure how to answer this. I know that cubes have a real root and a couple imaginary. So…
JCase
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difference consecutive perfect roots

i have found a relationship between the indices of perfect roots (eg. 1,4,9,25). if you find the difference between consecutive perfect roots of any index and find the difference between those differences and so on, you eventually get one number.…
mkdude
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