document.write( "Question 997365: Find a degree 3 polynomial with coefficient of x^3 equal to 1 and zeros -1, -4 i and 4 i. \n" ); document.write( "

Algebra.Com's Answer #615491 by MathLover1(20850) $\"\"$ $\"About$

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a degree $\"3\"$ polynomial with coefficient of $\"x%5E3\"$ equal to $\"1\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E3%2Bbx%5E2%2Bcx%2Bd\"$ \r
\n" ); document.write( "\n" ); document.write( "if given zeros $\"x%5B1%5D=-1\"$ , $\"x%5B2%5D=-4i\"$ and $\"x%5B3%5D=4i\"$ , we will use zero product formula\r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=%28x-+x%5B1%5D%29%28x-+x%5B2%5D%29%28x-+x%5B3%5D%29\"$ ....plug in given values\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=%28x-+%28-1%29%29%28x-%28-4i%29%29%28x-+4i%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=%28x%2B1%29%28x%2B4i%29%28x-+4i%29\"$ .....recall, $\"%28x%2B4i%29%28x-+4i%29=x%5E2-%284i%29%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=%28x%2B1%29%28x%5E2-+%284i%29%5E2%29\"$ ....since $\"%284i%29%5E2%29=4%5E2%2A%28i%29%5E2=16%28-1%29=-16\"$ , we have\r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=%28x%2B1%29%28x%5E2-+%28-16%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=%28x%2B1%29%28x%5E2%2B16%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E3%2B16x%2Bx%5E2%2B16\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E3%2Bx%5E2%2B16x%2B16\"$ \r
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