document.write( "Question 562138: If you have a polynomial that has roots at -2 (single root), 1 (double root) and 3 (single root), what is the exact equation of the polynomial passing through the point (-4,210)?
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #364486 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
The polynomial must have factors $\"x-%28-2%29\"$ = $\"x%2B2\"$ ,
\n" ); document.write( " $\"%28x-1%29%5E2\"$ , and $\"x-3\"$ .
\n" ); document.write( "If it is a polynomial of degree 4, it will be
\n" ); document.write( " $\"P%28x%29=a%28x%2B2%29%28x-1%29%5E2%28x-3%29\"$
\n" ); document.write( "If we also know that $\"P%28-4%29=210\"$
\n" ); document.write( "

,
\n" ); document.write( "then $\"a\"$ = $\"210%2F350\"$ = $\"3%2F5\"$
\n" ); document.write( " $\"P%28x%29=%283%2F5%29%28x%2B2%29%28x-1%29%5E2%28x-3%29\"$ = $\"%283%2F5%29%28x%5E4-3x%5E3-3x%5E2%2B11x-6%29\"$
\n" ); document.write( "There are also infinite other polynomials with the same roots passing through the same point. For example,
\n" ); document.write( " $\"G%28x%29=%283%2F10%29%28x%5E2%2B4%29%28x%2B2%29%28x-1%29%5E2%28x-3%29\"$ has exactly the same roots and complies with $\"G%28-4%29=210\"$ , but its degree is 6,and it's probably not the intended answer. \n" ); document.write( "

\n" );