SOLUTION: Find a thrid-degree polynomial with rational coefficients that has roots -5 and 6 + i.

Question 196688: Find a thrid-degree polynomial with rational coefficients that has roots -5 and 6 + i.
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
Remember that when an imaginary term is a solution, the complex conjugate is also
.
x=(-5) ,,,,(x+5)=0
.
x= ( 6+i),,,(x-(6+i) ) =0,,,,(x-6-i) =0
.
and x=(6-i),,,, (x - (6-i) ) = 0,,,,(x-6+i) =0
.
combining
.
(x+5)(x-6-i) ( x-6+i ) =0
.
(x+5) ( x^2 -6x +ix -6x +36 -6i -xi+6i -i^2 )
.
(x+5) ( x^2 -12x +37)
.
x^3 -12x^2 +37x +5x^2 -60x +185
.
x^3 -7x^2 -23x +185
.
checking
.
with x=0,, both original and answer =185
.
with x=1, both are 156 ,,,,,ok
.
Revised mon 5-18
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