document.write( "Question 62800: the degree three polynomial f(X) with real coefficients and leading coefficient 1, has 4 and 3+ i among roots. express f(X)as a product of linear and quardratic olynomials with real coefficients. \n" ); document.write( "

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the degree three polynomial f(X) with real coefficients and leading coefficient 1, has 4 and 3+ i among roots. express f(X)as a product of linear and quardratic olynomials with real coefficients.
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\n" ); document.write( "The linear polynomial (x - 4)
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\n" ); document.write( "Find the quadratic:
\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( "x^2 - 6x + 9 = -1
\n" ); document.write( "x^2 - 6x + 9 + 1 = 0
\n" ); document.write( "x^2 - 6x + 10 = 0
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\n" ); document.write( "mult (x - 4) * (x^2 - 6x + 10) = x^3 - 10x^2 + 34x - 40
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\n" ); document.write( "f(x) = x^3 - 10x^2 + 34x - 40 \n" ); document.write( "

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