document.write( "Question 1068321: Find a polynomial f (x) of degree 3 with real coefficients and the following zeros. 4, 3+i\r
\n" ); document.write( "\n" ); document.write( "f (x) = _____\r
\n" ); document.write( "\n" ); document.write( "Appreciate help on this question. I believe it is asking for zeros, only two zeros given, need to find the third zero. ( think that is what this question is asking). Need step-by-step solution. \n" ); document.write( "
Algebra.Com's Answer #683571 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
Find a polynomial f (x) of degree 3 with real coefficients and the following zeros. 4, 3+i
\n" ); document.write( ":
\n" ); document.write( "from the zeros given we can make two factors
\n" ); document.write( "x = 4
\n" ); document.write( "(x-4) = 0
\n" ); document.write( "and
\n" ); document.write( "x = 3 + i
\n" ); document.write( "x - 3 = i
\n" ); document.write( "Square both sides
\n" ); document.write( "(x-3)^2 = i^2
\n" ); document.write( "FOIL (x-3()x-3), i^2 is -1
\n" ); document.write( "x^2 - 6x + 9 = -1
\n" ); document.write( "x^2 - 6x + 9 + 1 = 0
\n" ); document.write( "x^2 - 6x + 10 = 0
\n" ); document.write( "Make an equation using these two factors
\n" ); document.write( "f(x) = (x-4)*(x^2-6x+10)
\n" ); document.write( "multiply these two factors, results:
\n" ); document.write( "f(x) = x^3 - 10x^2 + 34x - 40 \n" ); document.write( "
\n" );