document.write( "Question 765031: Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
\n" ); document.write( "7, -11, and 2 + 8i\r
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\n" ); document.write( "\n" ); document.write( "State how many imaginary and real zeros the function has.\r
\n" ); document.write( "\n" ); document.write( "f(x) = x^4 - 8x^3 + 17x^2 - 8x +16 \n" ); document.write( "

Algebra.Com's Answer #465924 by DrBeeee(684) $\"\"$ $\"About$

You can put this solution on YOUR website!
All complex roots (zeroes) come in PAIRS. You need to include 2 - 8i as one of the four zeroes. Then we have the factored form of the polynomial is
\n" ); document.write( "(1) $\"%28x-7%29%2A%28x%2B11%29%2A%28x-2%2B8i%29%2A%28x-2-8i%29\"$
\n" ); document.write( "Just FOIL the first two factor and FOIL the last factors to get
\n" ); document.write( "(2) $\"%28x%5E2%2B4x-77%29%2A%28x%5E2-4x%2B68%29\"$
\n" ); document.write( "Now multiply the two quadratics of (2) and get
\n" ); document.write( "(3) $\"x%5E4%2B0%2Ax%5E3-25x%5E2%2B580x-5207\"$
\n" ); document.write( "This function (3) has two real zeroes, 7 and -11 and a complex pair of zeroes, 2+8i and 2-8i \n" ); document.write( "

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