document.write( "Question 1114694: Find the polynomial with degree 5. Zeros -2,1,2,i. Y-int of (0,-8) \n" ); document.write( "

Algebra.Com's Answer #729606 by Boreal(15235) $\"\"$ $\"About$

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The factors are (x+2)(x-2)(x-1), (x-i) and (x+i), because if i is a factor, -i is also a factor
\n" ); document.write( "This is (x^2-4)(x-1)and (x^2+1), the latter giving rise to roots of +/- i
\n" ); document.write( "That is (x^4-3x^2-4)(x-1), or
\n" ); document.write( "x^5-x^4-3x^3+3x^2-4x+4
\n" ); document.write( "or a(x^5-x^4+3x^2-4x+4)=-8, when x=0
\n" ); document.write( "so 4a=-8 and a =-2
\n" ); document.write( "polynomial is -2(x^5-x^4+3x^2-4x+4) ANSWER
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