document.write( "Question 1075736: Write 3+i,2,-4 into a polynomial equation \n" ); document.write( "

Algebra.Com's Answer #690400 by Boreal(15235) $\"\"$ $\"About$

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If a root is 3+i, there is a root 3-i, because complex roots are conjugate pairs.
\n" ); document.write( "Two factors are (x-2)(x+4)
\n" ); document.write( "To get roots of 3+/- i, we need b=-6 and sqrt(b^2-4ac) to equal sqrt(-4) since we are dividing by 2 and that will give +/- i
\n" ); document.write( "b^2=36, a is 1, so c must be 10 so that 4c=40
\n" ); document.write( "(x^2-6x+10) is the quadratic
\n" ); document.write( "The polynomial is (x^2+2x-8)(x^2-6x+10)
\n" ); document.write( "or x^4-4x^3-10x^2+68x-80.
\n" ); document.write( " $\"graph%28300%2C300%2C-10%2C10%2C-250%2C200%2Cx%5E4-4x%5E3-10x%5E2%2B68x-80%29\"$ \n" ); document.write( "

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