Find the roots of polynominal equations with Purpose Excel Functions
Quartic - ax^4 + bx^3 + cx^2 + dx +e = 0
=quartic(a, b, c, d, e, Output Index -1 to 5 (optional))
Cubic - ax^3 + bx^2 + cx + d = 0
=cubic(a, b, c, d, Output Index -1 to 4 (optional))
CubicCa - x^3 + bx^2 + cx + d = 0
=cubicC(a, b, c, d, Output Index -1 to 4 (optional))
Quadratic - ax^2 + bx + c = 0
=quadratic(a, b, c, Output Index 1to 3(optional))
1 Enter an output index to specify a real root number, or the number of real roots
2 Enter a negative output index to specify a complex root number, or the number of complex roots
3 Enter as an array formula to return an array with the real part of all roots and the number of real roots
4 Enter as an array formula with output index = -1 to return an array with the imaginary part of all roots and the number of complex roots
5 Equations of lower order may be solved by entering 0 in the redundant factors.
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If you have a quartic equation: ax^4 + bx^3 + cx^2 + dx +e = 0, then enter the values for the coefficients a to e in five separate cells, say A1 to A5, then the four solutions to the equation are given by:
=quartic(A1, A2, A3, A4, A5, 1) through to:
=quartic(A1, A2, A3, A4, A5, 4)
and the number of real roots is given by
=quartic(A1, A2, A3, A4, A5, 5)
You can also enter
=quartic(A1, A2, A3, A4, A5) in one cell, then select that cell and the three below, and press ctrl-shift-enter, and this will return all four roots of the equation.
Hope that helps
Having gone through your excellent and impressive spreadsheet, I find I must do what is nearly the unthinkable. Please tell me how to get started, an example would be fine.