# Questions tagged [cubic-equations]

This tag is for questions relating to cubic equations, these are polynomials with $~3^{rd}~$ power terms as the highest order terms.

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### when do Lagrange resolvents work to solve a polynomial such as the following:

y^3 - 3y^2 - 3y + 1 = 0 to this one it works but when i try it on the one below : y^3 - 2y^2 + 1 = 0 the Jagrange resolvent technique does not work, I would like to know why.
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### Challenger Theory Of Questions question

Let $y = P(x)$ be polynomial of degree $4$ such that $P(1) = 2$ and attains min value 1 at both $x=1$ and $x=2$. Then $P'(1)=$ a)$-1$ b)$2$ c)$0$ d)$1$ According to me graph of $4^{th}$ degree ...
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### What is the integral of an inverse square root of a standard cubic formula?

$$\int\frac{1}{\sqrt{ax^3+bx^2+cx+d}}dx$$ I know the solution to the integral of an inversed square root of a quadratic equation. But I am not being able to solve this one and I have searched ...
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### For which $a, b$ in $(-1,1)$ does $\frac{1}{3}x^3-a^2x+b=0$ have three real solutions?

I know $\frac{1}{3}x^3-a^2x+b=0$ will always have one solution as $\frac{-b}{x} = \frac{1}{3}x^2-a^2$ will always have one intersection in the upper two quadrants of the coordinate system. But I can'...
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### Solving $x³+24x²+5x-13 = 0$ [closed]

I have been doing some mathematics and I have come across this question that I need to somehow solve to move onto the next questions. I'm currently undertaking an abstract algebra unit with this ...
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### Solving $x^3 + 12x^2 + 8x − 7 = 0$

I have been doing some maths and I have come across this question that I need to somehow solve to move onto the next questions: $$x^3 + 12x^2 + 8x − 7 =0$$ Can anyone help and solve with a step by ...
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### Cubic Discriminant Uses

The discriminant for cubic equations is - $Δ​\:=b^22\:^2−4ac^3−4b^3d−27a^2d^2+18abcd$ And I am aware that you can determine the number of roots a cubic has using method shown below - $Δ​\:>0$ ...
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### Solve the Cubic $x^3+24x^2+6x-4$

I'm having trouble solving this cubic: $x^3+24x^2+6x-4$. Is anyone able to help explain how to get the values of $x$?
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### Lagrange Method of Solving Cubic Equations

Let $K$ be a field (for simplicity, one may assume $K\subseteq\mathbb{C}$), and let $d\in K$. Denote $w=\sqrt{d}$, and $\zeta=(-1+\sqrt{-3})/2$. If $f(x)=x^3+ax^2+bx+c$ is the minimal polynomial of ...
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### A series of multiplication leads to $\frac{1}{2} = 2$

I'm presented with the equation $\frac{a+b}{a} = \frac{b}{a+b}$ Performing cross multiplication yields $a^2+2ab+b^2 = ab$ Subtracting $ab$ from both sides, we get $a^2+ab+b^2 = 0$ Multiplying both ...
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### solution of the cubic equation $x^3 = 0$?
it is clear that one solution of the above equation is $x = 0$, but since it is a cubic equation so it should have $3$ complex roots, so what will be its other roots? Also how can we determine that a ...