SOLUTION: I need help with this: find a polynomial with integer coefficients that has the given zeros -4, -1+i, -1-i

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Question 86379: I need help with this: find a polynomial with integer coefficients that has the given zeros -4, -1+i, -1-i
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
I need help with this: find a polynomial with integer coefficients that has the given zeros -4, -1+i, -1-i
CONJUGATE ROOTS ARE -1+I AND -1-I
SO EQN. FOR THESE 2 ROOTS IS
[X-(-1+I)][X-(-1-I)]=0=(X+1)^2-I^2=X^2+2X+1+1=0=X^2+2X+2=0
NOW THIRD ROOT IS REAL -4
SO MULTIPLY THE ABOVE WITH X+4 TO GET THE POLYNOMIAL
(X+4)(X^2+2X+2)=0
X^3+2X^2+2X+4X^2+8X+8=0
X^3+6X^2+10X+8=0