document.write( "Question 1002112: Find a 4th degree polynomial with zeroes of 2,-2,3i and f(0)=-108. Our math book doesn't explain anything on how to solve this, I have searched online and believe I have the solution. I want some verification if i am correct or not.\r
\n" ); document.write( "\n" ); document.write( "f(x)=(x-3i)(x+3i)(x+2)(x-2)
\n" ); document.write( "(x^2+9)(x^2-4)
\n" ); document.write( "(x^4-5x-36)\r
\n" ); document.write( "\n" ); document.write( "I am unsure for the rest. and what to do with f(0)=-108 \n" ); document.write( "

Algebra.Com's Answer #619098 by ikleyn(52776) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "Find a 4th degree polynomial with zeroes of 2,-2,3i and f(0)=-108.
\n" ); document.write( "Our math book doesn't explain anything on how to solve this, I have searched online and believe I have the solution.
\n" ); document.write( "I want some verification if i am correct or not.
\n" ); document.write( "f(x)=(x-3i)(x+3i)(x+2)(x-2)
\n" ); document.write( "(x^2+9)(x^2-4)
\n" ); document.write( "(x^4-5x-36)
\n" ); document.write( "I am unsure for the rest. and what to do with f(0)=-108
\n" ); document.write( "---------------------------------------------------------------------\r
\n" ); document.write( "\n" ); document.write( "

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document.write( "f(x)=(x-3i)(x+3i)(x+2)(x-2)     this line is correct.\r\n" );
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document.write( "(x^2+9)(x^2-4)                  this line is correct.\r\n" );
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document.write( "(x^4-5x-36)                     this line is incorrect. It should be (x^4+5x^2-36).\r\n" );
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document.write( "So far, you get the polynomial p(x) = x^4+5x^2-36.\r\n" );
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document.write( "Calculate its value at x = 0. Simply substitute x=0 into p(x). You will get\r\n" );
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document.write( "p(0) = 0^4 +5*0^2 - 36 = -36.\r\n" );
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document.write( "Therefore, apply the factor 3 to p(x): f(x) = 3*p(x) to get the polynomial f(x) which has the same zeroes as p(x) \r\n" );
document.write( "and has the value f(0) = -108 at x=0.\r\n" );
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document.write( "Now your polynomial and your answer is f(x) = 3*(x^4+5x^2-36) = 3x^4 + 15x^2 - 108.\r\n" );
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