Help to find the solution with steps

label Algebra
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Find a polynomial function with real coefficients that has the indicated zeros and satisfies the given condition: Zeros :2 + 5i,i ; Degree: 4

 

May 21st, 2015

degree = 4

number of zeroes = 4

zeroes = 2 + 5i , 2 - 5i  , i , - i

polynomial = { x - (2 + 5i) }{x - (2 - 5i) }(x + i)(x - i)

     = ( x - 2 - 5i)(x - 2 + 5i)(x^2 - i^2)

  = (x^2 - 4x + 29)(x^2 + 1) ,  i^2 = - 1

= x^4 - 4x^3 + 30x^2 - 4x + 29

May 21st, 2015

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May 21st, 2015
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May 21st, 2015
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