Roots of polynomials of degree 3 - cubics
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Cubic equations
[Equation goes here - download the original to see it.] [Equation goes here - download the original to see By equating coefficients we obtai [Equation goes here - download the original to see it.] [Equation goes here - download the original to see it.] [Equation goes here - download the original to see it.] The roots, cannot be found directly by means of these equations. Any attempt to solve them simultaneously merely regenerates the original equation in some form. However, if additional information is available, then these equations may provide a shortcut to the roots. We use the symbol [Equation goes here - download the original to see it.] Using these symbols we can prove a number of identities. [Diagram goes here - download the original to see it.] Proof [Equation goes here - download the original to see it.] [Equation goes here - download the original to see it.] Proof [Equation goes here - download the original to see it.] [Equation goes here - download the original to see it.] Proof [Equation goes here - download the original to see it.] [Equation goes here - download the original to see it.] Example [Equation goes here - download the original to see it.] Solution [Equation goes here - download the original to see it.] [Diagram goes here - download the original to see it.] [Equation goes here - download the original to see it.] Quartic equations [Equation goes here - download the original to see it.] Example Prove the following identities for quartics [Equation goes here - download the original to see it.] Solution [Equation goes here - download the original to see it.] [Equation goes here - download the original to see it.] [Equation goes here - download the original to see it.] [Equation goes here - download the original to see it.] [Equation goes here - download the original to see it.] [Equation goes here - download the original to see it.] [Equation goes here - download the original to see it.] Example [Equation goes here - download the original to see it.] Solution [Equation goes here - download the original to see it.] [Equation goes here - download the original to see it.] [Equation goes here - download the original to see it.] [Equation goes here - download the original to see it.] [Equation goes here - download the original to see it.] [Equation goes here - download the original to see it.] [Equation goes here - download the original to see it.] [Equation goes here - download the original to see it.] [Equation goes here - download the original to see it.] [Equation goes here - download the original to see it.] [Equation goes here - download the original to see it.]
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Contents of
Roots of polynomials of degree 3 - cubics
1 Roots and linear factors
2 Cubic equations
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