Apolynomial with rational coefficients has roots 5 and -6i. (the i is an imaginary number not variable). what is the polynomial? with work shown

The answer is  {-(5) (36)× -(180)

Step-by-step explanation:

   A polynomial with rational coefficients has roots 5 and -6i (There i is the    

   imaginary number not variable )

   As we knew that imaginary no comes in pair . This means that if  -6i is

   one root then the other root will be 6i

   So if we assume the lowest polynomial that is possible is given as

    {-(sum of all roots) +(roots taken two at a time)

    -(product of all roots)

    {-(5+6i+(-6i)) +(5×6i +5×(-6i) +6i×(-6i))

    -(5×6i×(-6i))

    = -1

    {-(5) (36)× -(180)

   The general case we assume that the three previous roots and rest roots

   a4,a5,a6 ...............an

  -(sum of all roots)× +(roots taken two at a  

   time) ×- .......................................... (product of all roots)

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