document.write( "Question 781983: find a degree 3 polynomial with coefficient of x^3 equal to 1 and zeros 2,-5i and 5i \n" ); document.write( "

Algebra.Com's Answer #476193 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " $\"ax%5E3%2Bbx%5E2%2Bcx%2Bd=0\"$ where $\"a=1\"$ \r
\n" ); document.write( "\n" ); document.write( "so, your polynomial will be $\"x%5E3%2Bbx%5E2%2Bcx%2Bd=0\"$ \r
\n" ); document.write( "\n" ); document.write( "use zero product rule since you are given zeros $\"x%5B1%5D=2\"$ , $\"x%5B2%5D=-5i\"$ and $\"x%5B3%5D=5i\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x-2%29%28x-%28-5i%29%29%28x-5i%29=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x-2%29%28x%2B5i%29%28x-5i%29=0\"$ ...... $\"%28x%2B5i%29%28x-5i%29=x%5E2-%285i%29%5E2=x%5E2-%2825%28-1%29%29=x%5E2%2B25\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x-2%29%28x%5E2%2B25%29=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x%5E3%2B25x-2x%5E2-50=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x%5E3-2x%5E2%2B25x-50=0\"$ \r
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