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Dowland
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Cool, and thanks for your kind words epenguin. And thank you so much for your help, Dick and epenguin, I am grateful to you for you took the time and effort to help me with this!
The discriminant of a cubic equation is a mathematical term that is used to determine the nature of the roots of the equation. It is calculated using the coefficients of the equation and can help determine if the equation has real or imaginary roots.
The discriminant of a cubic equation can be calculated using the formula D = b^2c^2 - 4ac^3 - 4b^3d - 27a^2d^2 + 18abcd, where a, b, c, and d are the coefficients of the cubic equation ax^3 + bx^2 + cx + d = 0.
A positive discriminant indicates that the cubic equation has three distinct real roots. This means that the equation crosses the x-axis three times and has three solutions.
A negative discriminant indicates that the cubic equation has one real root and two complex roots. This means that the equation does not cross the x-axis and has only one real solution.
A zero discriminant indicates that the cubic equation has at least two equal real roots. This means that the equation touches the x-axis at two points and has two equal solutions.