document.write( "Question 87744: This is really tough. Find the solution polynomial P(x) given zeros at: i, and – 3 +√3 (assume P(x) has rational coefficients). \n" ); document.write( "

Algebra.Com's Answer #63906 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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Find the solution polynomial
\n" ); document.write( "P(x) given zeros at: i, and – 3 +√3 (assume P(x) has rational coefficients).
\n" ); document.write( ":
\n" ); document.write( "x = i
\n" ); document.write( "x^2 = i^2; square both sides:
\n" ); document.write( "x^2 = -1; remember that i^2 = -1
\n" ); document.write( "x^2 + 1 = 0; add one to both sides,
\n" ); document.write( "One factor is (x^2 + 1)
\n" ); document.write( ":
\n" ); document.write( "x = -3 + Sqrt(3)
\n" ); document.write( "x + 3 = Sqrt(3); added 3 to both sides
\n" ); document.write( "(x+3)^2 = 3; squared both sides
\n" ); document.write( "x^2 + 6x + 9 = 3; FOILed (x+3)^2
\n" ); document.write( "x^2 + 6x + 9 - 3 = 0; subtract 3 both side
\n" ); document.write( "x^2 + 6x + 6 = 0; the 2nd factor
\n" ); document.write( ":
\n" ); document.write( "Multiply (x^2 + 6x + 6) times (x^2 + 1)
\n" ); document.write( ":
\n" ); document.write( "you should get: P(x) = x^4 + 6x^3 + 7x^2 + 6x + 6 \n" ); document.write( "

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