This problem illustrates Girard’s geometric interpretation of negative solutions

Question

This problem illustrates Girard’s geometric interpretation of negative solutions to polynomial equations. Let two straight lines DG, BC intersect at right angles at O (Fig. 14.19). Determine A on the line bisecting the right angle at O so that ABOF is a square of side 4. Draw ANC as in the diagram so that NC=?153. Find the length FN. (Girard notes that if x = FN, then x^4=8x^3+12x^2+128x-256 and so there are four possible solutions, each of which can be calculated. The two positive solutions are represented by FN and FD, while the two negative ones are represented by FG and FH, the latter two taken in the opposite direction from the former two.)

Explanation / Answer

solutions of this quartic equation x^4=8x^3+12x^2+128x-256 are 10.173208,1.572759,other two are complex roots since FD>FN and both are positive FD=10.173208 and FN=1.572759

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.