document.write( "Question 1135463: Form a polynomial f(x) with real coefficients having the given degree and zeros Degree 4; zeros: 1, multiplicity 2;4i \n" ); document.write( "

Algebra.Com's Answer #753061 by Boreal(15235) $\"\"$ $\"About$

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multiplicity 2 means squared and zero of 1 means factor x-1
\n" ); document.write( "(x-1)^2 is part of this
\n" ); document.write( "4i is a root, so -4i is one
\n" ); document.write( "factors are (x-4i) and (x+4i)
\n" ); document.write( "they multiply to x^2+16
\n" ); document.write( "the other multiplies to (x^2-2x+1)
\n" ); document.write( "the polynomial is x^4-2x^3+x^2+16x^2-32x+16
\n" ); document.write( "or x^4-2x^3+17x^2-32x+16
\n" ); document.write( " $\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E4-2x%5E3%2B17x%5E2-32x%2B16%29\"$ \n" ); document.write( "

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