# Tagged Questions

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

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### How to Solve a “Cubic Equation”? [on hold]

-Hello, Guys! How to solve a "Cubic Equation"?
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### Formula for solutions of a cubic equation [duplicate]

I am looking for a simplified formula for a cubic equation in the form: $$Ax^3+Bx^2+Cx+D=0$$ That solves for roots $r_1, r_2$, and $r_3$ when the discriminant is positive and $r$ when it is ...
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### The cubic equation $x^3-5x^2+6x-3 = 0$ has solutions $\alpha$, $\beta$ and $\gamma$. [on hold]

The cubic equation $x^3-5x^2+6x-3 = 0$ has solutions $\alpha$, $\beta$ and $\gamma$. Find the value of $$\frac{1}{\alpha^2}+\frac{1}{\beta^2}+\frac{1}{\gamma^2}$$
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### If $a>b>0$ and $a^3 +b^3 +27ab=729$ then the quadratic equation $ax^2+bx-9=0$ has roots $P,Q(P<Q)$. Find the value of $4Q-aP$?

If $a>b>0$ and $a^3 +b^3 +27ab=729$ then the quadratic equation $ax^2+bx-9=0$ has roots $P,Q(P<Q)$. Find the value of $4Q-aP$? How will I begin with the solution just a hint would be enough....
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### Find the limit when X--->2

Please HELP. I've tried doing it with L'Hopital but I can't. The answer is supposed to be 1/3 .Please help. $$\lim_{x\to 2/3} \frac{\sqrt[3]{9x^7+ 4}- 2 }{3x-2}$$
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### Solving a Linear Recurrence with a Cubic Characteristic Equation

I've been learning Linear Recurrences in my Discrete Math course and I've learned how to solve them when the characteristic equation is a quadratic. Is solving a linear recurrence with a cubic ...
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### Cubic's Irreducible case.

I know how to solve a cubic equation using Cardano's method, but some equation when solved through Cardano's method give complex numbers under a cube root sign. For Example: $x^3-15x=4$. I want to ...
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### Why does the “printing neatly” algorithm use cubes rather than squares?

In Introduction to Algorithms, 2nd ed. (Cormen, Leiserson, Rivest, and Stein), ch. 15, Dynamic Programming, problem 15-2 Printing neatly (a copy of which is here), the official solution given in ...
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### non-complex cubic roots formula?

Suppose we have a cubic equation $$ax^3 +bx^2 +cx +d =0$$ for which we know that all three distinct roots are real. Do we have a formula for them that does not involve complex roots of unity? The ...
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### Integrating Inverse square root of a polynomial

I'm Looking for integrals of the following kind $\int\limits_{0}^{M} \left( -x^3 +bx^2 -\omega \right)^{-\frac{1}{2}} \,dx \, ,$ for positive constants $b, \omega$, and $M$ is on of the roots of ...
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### Precision in Cubic spline interpolation

I am working on cubic spline interpolation with set of data points from CAD with following steps: Form piecewise spline equations between points. cubic equation : $ax^3 + bx^2 +cx + d = P(x)$ ...
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### Solving a cubic equation by factorization

I have the cubic equation $G^3 - (C - C_0)G - \frac{F}{\eta}$, with the constants $C, C_0, F, \eta \in \Re$. I want to find the solutions, so I tried factorising the equation, but I have after ...
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### Deriving Formulae for the roots of the quartic and cubic polynomials

I have seen derivations of the general solution for the roots of fourth and third degree polynomials of 1 variable in Dummit & Foote's Abstract Algebra; however, it was by no means simple to me. I ...
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### How would you find the exact roots of this equation?

My friend asked me what the roots of $y=x^3+x^2-2x-1$ was. I didn't really know and when I graphed it, it had no integer solutions. So I asked him what the answer was, and he said that the $3$ roots ...
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### Difference between real and complex solutions of cubic equations [closed]

Take for an example, this equation. $$x^3+15x+4=0$$ This equation has two complex solutions and a real one. $$x≈0.1327-3.8798i$$ $$x≈0.1327+3.8798i$$ $$x≈-0.26542$$ What's extra in the complex ...