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\n" ); document.write( "The statement of the problem is not complete. Without the stated requirement that the polynomial have rational coefficients, the fourth root could be any complex number.
\n" ); document.write( "Assuming rational coefficients, the four roots are -4, -4, 5+5i, and 5-5i.
\n" ); document.write( "The quadratic polynomial with roots -4 and -4 is
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\n" ); document.write( "The quadratic polynomial with roots 5+5i and 5-5i is
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\n" ); document.write( "An alternative way to find the quadratic polynomial with roots 5+5i and 5-5i is to use the fact that the quadratic polynomial ax^2+bx+c has roots whose sum is -b/a and whose product is c/a.
\n" ); document.write( "The sum of the roots 5+5i and 5-5i is 10; so the linear coefficient in the quadratic polynomial is -10.
\n" ); document.write( "The product of the roots 5+5i and 5-5i is 25-25i^2 = 25+25 = 50; so the constant in the quadratic polynomial is 50.
\n" ); document.write( "Then the quadratic polynomial with roots 5+5i and 5-5i is x^2-10x+50.
\n" ); document.write( "Finally the polynomial with roots -4, -4, 5+5i and 5-5i is
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