# Quartic2.xls

Rating:
3

### Description

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))

Notes
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.

Courtesy of Interactive Design Services Pty Ltd - a small civil engineering consultancy based in Sydney, Australia, specializing in analysis, design, review and technical advice related to bridges and soil interaction structures such as retaining walls and buried structures. The principal of the company, Doug Jenkins, has over 30 years experience in the design and construction of bridges, retaining walls, and buried arch structures.

Calculation Reference
Polynominal

02 Jul 2008
02 Jul 2008
File Size:
117.00 Kb
302
File Version:
1.0
File Author:
Doug Jenkins
Rating:
3

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DougJenkins 15 years ago
Claiborne - The quartic (and other) functions work just like a built in Excel function.
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
Doug
DougJenkins 15 years ago
Hello Doug,
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.
Respectfully,
Claiborne