Polynomials

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Created by
Jack H

Cards (8)

  • a2+a^2 +b2= b^2 = (a+ib)(a−ib)(a + ib)(a - ib)
  • If one solution to a polynomial with real coefficients is complex, then another solution will be its conjugate
  • (x - z)(x - z*) = x2−2xRe(z)+x^2 -2xRe(z) +∣z∣2 |z|^2
  • For a quadratic with roots p and q:
    ∑p=\sum p =−b/a -b/a
    ∑pq=\sum pq =c/a c/a
  • For a cubic with roots p, q and r:
    ∑p=\sum p =−b/a -b/a
    ∑pq=\sum pq =c/a c/a
    ∑pqr=\sum pqr =−d/a -d/a
  • For a quartic with roots p,q,r and s:
    ∑p=\sum p =−b/a -b/a
    ∑pq=\sum pq =c/a c/a
    ∑pqr=\sum pqr =−d/a -d/a
    ∑pqrs=\sum pqrs =e/a e/a
  • If an equation in x has a root x = p, and if we make a substitution u = f(x), then the resulting equation in u has a root u = f(p)
  • To carry out substitution:
    1. Create an equation showing the relationship between u and x, and make x the subject
    2. Replace x for u in the polynomial using the relationship
    3. Manipulate to get a polynomial in u with the required order
    4. Rearrange to get a polynomial that is equal to 0