Descartes' rule of signs

Intros
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Lessons
  1. Fundamental Theorem of Algebra VS. Descartes' Rule of Signs
  2. Descartes' Rule of Signs – explained.
    exercise: Use Descartes' Rule of Signs to determine the possible combinations of roots of:
    P(x)=2x6−7x5+x4+5x3−6x2−10P(x)=2x^6-7x^5+x^4+5x^3-6x^2-10
Examples
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Lessons
  1. Use Descartes' Rule of Signs to Determine the Number of Positive and Negative Roots
    Use Descartes' Rule of Signs to determine the possible number of positive roots and negative roots:
    1. P(x)=4x+9x6−5x2−10x7+6x3−8x5−7x4+3 P(x)=4x+9x^6-5x^2-10x^7+6x^3-8x^5-7x^4+3
    2. P(x)=x4−5x2−6x P(x)=x^4-5x^2-6x (note: NO constant term!!)
  2. Use the Rational Roots Theorem, together with Descartes' Rule of Signs, to Find Roots Effectively
    Solve:
    1. −3x3+22x2−37x+10=0 -3x^3+22x^2-37x+10=0
    2. −3x3−5x−7x2+2x4−3=0 -3x^3-5x-7x^2+2x^4-3=0