# Questions tagged [cubic-equations]

These are polynomials with 3rd power terms as the highest order terms. Usually used with polynomial tag.

776 questions
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### Let : $P(x)=x^{3}+ax^{2}+bx+c$ where $(a,b,c)\in Z^3$

Question : If : $P(x)=x^3+ax^2+bx+c$ where $(a,b,c)\in Z^3$ And $m,n,k$ root of $P(x)$ such that : $m.n=k$ Then show that : $2P(-1)$ multiple of $P(1)+P(-1)-2[1+P(0)]$ My try : We known ...
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### Equation : $3x^4+x^3-10x^2-x+3=0$ [duplicate]

Solve in $R$ the following equation : $3x^4+x^3-10x^2-x+3=0$ Im try use sub $y=x+\frac{1}{x}$ But I don't understand whene and where I use this sub Please give me ideas or hint to approach it
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### Solve in $C$ : $p(x)=x^4+2x^3-x^2-2x+7=0$ [duplicate]

Find all root : $p(x)=x^4+2x^3-x^2-2x+7=0$ Where $p(\alpha)=0$ , $\alpha=\sqrt{2}+\omega$ $\omega=e^{\frac{2iπ}{3}}$ My try : Since : $\alpha$ root of equation then $\bar\alpha$ also root ...
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### Finding all prime $p$ for which there exists a positive integer $n$ such that $p^n+1$ is a perfect square?

$p=7~(n=1)$ is a solution. But how to prove that there are not any other solutions?
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### How can we solve the expression explicitly for $X$ in terms of $Y$?

I am thinking how to write $X$ explicitly in terms of $Y,A,B,C$? I have $AX^3 + X^2(B-1) + X(-C) + \alpha = Y$ I thought of using symbolic maths but could not find any. Any help is nice!
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### Roots of a cubic polynomial in $[-1,1]$ [closed]

I am preparing for an entrance and this question has taken too much of my time. Suppose function $f : \mathbb R \to \mathbb R$ is given by $$f(x) = x^3 - 3x + b$$ Find the number of points in the ...
### How to solve the cubic equation $-1.6x^3-2.1x^2-2.9x-0.3=0$
Is there any method similar to the quadratic formula to solve the equation; {$-1.6x^3-2.1x^2-2.9x-0.3=0$} If not, how would I go about finding the solutions for cubic equations like these?