text: # Imaginary Coefficients
  
  • Nov 4th 2009, 04:19 PM
  SHiFT
  Imaginary Coefficients
  Find a possible polynomial p(x) such that the degree of p(x) is 3 and all of the coefficients are imaginary.
  • Nov 4th 2009, 04:33 PM
  skeeter
  Quote:
  
  Originally Posted by SHiFT
  Find a possible polynomial p(x) such that the degree of p(x) is 3 and all of the coefficients are imaginary.
  
  imaginary coefficients? first I've heard of a problem like this.
  
  $p(x) = ix^3 + 2ix^2 + 3ix + 4i = i(x^3 + 2x^2 + 3x + 4)$
  • Nov 4th 2009, 04:49 PM
  SHiFT
  Sorry, I also forgot to include that in the directions it says let p(x) be a polynomial such that p(-1)=0 and p(3)=0
  • Nov 5th 2009, 03:29 AM
  HallsofIvy
  Quote:
  
  Originally Posted by SHiFT
  Sorry, I also forgot to include that in the directions it says let p(x) be a polynomial such that p(-1)=0 and p(3)=0
  
  Just a minor detail, right?(Rofl)
  
  Okay that means that x+1 and x- 3 must be factors: write the polynomial as [tex](ax+ b)(x+1)(x-3)= (ax+b)(x^2- 2x+ 1)= ax^3+ (b-2a)x^2+ (a-2b)x+ b[/quote]. Now choose a and b to be imaginary number such that neither b-2a nor a-2b is 0. a= b= i works nicely.
metadata: {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}