Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

polynomial question?

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2 Answers

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  • rotchm
    Lv 7
    2 months ago

    The correct answer is: 

    The question is ill posed, and has infinitely many solutions. 

    For instance,  let p(x)= 5x² + 6x + 2. Thus, p(1/(2-i)) = 5+2i.  

    And  p(-8/5 + i/5) = 5-2i.  

    Thus here, c=-8/5 & d=1/5. 

    If p(x) were a deg 1 poly " mx+b", then the solution for c&d is unique and was given to you by another respondent. 

  • 2 months ago

    1/(2 - i) = (2+i)/{(2-i)*(2+i)} = (2 +i)/5 = 2/5 + i/5

    P(2/5 + i/5) = 5 + 2i and the coeficients are real then 

    P(2/5 + i/5)  = k*2/5 + m*i/5 = 5 + 2i ---> k = 25/2,  m = 10

    then (c + di) = k*c +m*d i = 5 - 2i --> 25*c/2 = 5   10*d = -2

    d = -1/5  c = 2/5

    c + i d = 2/5 - 2 i

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