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cubic equation edge cases

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#polynomials #quadratics #cubics #roots-of-cubics #branching-rules
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Factorising a Cubic Polynomial

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#polynomials #factoring #cubics #roots-of-cubics
111
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Roots of $x^3-2=0$...

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#polynomials #roots-of-cubics
73
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What would the cubic formula be if roots never existed?

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#polynomials #roots #continued-fractions #roots-of-cubics
96
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Finding all possible roots of the equation

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#roots #diophantine-equations #cubics #roots-of-cubics
168
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If $f(x) =ax^3+bx^2+cx+d$ is a cubic equation with roots $\alpha,\beta,\gamma.$ Is there a way to find $\alpha^2\beta+\beta^2\gamma+\gamma^2\alpha?$

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#algebra-precalculus #polynomials #roots #roots-of-cubics
137
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Let $r,s,t$ are roots of the cubic equation $x^3+bx^2+cx+d=f(x)$ then write down $D=((r-s)(r-t)(s-t))^2$ in terms of $b, c, d$

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#algebra-precalculus #polynomials #contest-math #cubics #roots-of-cubics
74
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Deforming roots of a cubic polynomial

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#cubics #complex-dynamics #roots-of-cubics
57
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Range of an equation $y=\frac{(x-\alpha)(x^3-3x+1)}{x-\alpha}$

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#analysis #roots-of-cubics
245
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Is there the continuous real root of the cubic equation and is there a closed formula to present it?

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#polynomials #cubics #roots-of-cubics
314
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How to separate cubic equations into two conic sections: Deep dive into Omar Khayyam

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#algebraic-geometry #conic-sections #math-history #roots-of-cubics
117
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Further information on the reduction of cubic equations to a system of two conic sections

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#geometry #algebraic-geometry #conic-sections #cubics #roots-of-cubics
77
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Need help understanding cubic formula derivation by Daniel Rui

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#roots-of-cubics
90
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How many roots of $x(1-x)^{2}=s$ are there in $(0,1)$?

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#real-analysis #polynomials #symmetry #cubics #roots-of-cubics
79
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How to determine the order of the real roots of a cubic equation?

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#inequality #polynomials #cubics #roots-of-cubics

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