document.write( "Question 1188485: Find a possible formula for a polynomial f that has degree 2 or less, f(1)=f(4)=0 and f(2)=6. \n" ); document.write( "

Algebra.Com's Answer #819609 by greenestamps(13203) $\"\"$ $\"About$

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\n" ); document.write( "The solution from the other tutor is algebraically correct; but it is very inefficient.

\n" ); document.write( "Given that there are two roots at x=1 and x=4, and that the degree is to be 2 or less, we know that in fact it is degree 2.

\n" ); document.write( "And given those two roots, we know the polynomial is of the form

\n" ); document.write( " $\"f%28x%29=a%28x-1%29%28x-4%29\"$

\n" ); document.write( "To finish finding the polynomial, us the given information that f(2)=6:

\n" ); document.write( " $\"f%282%29=a%282-1%29%282-4%29=a%281%29%28-2%29=-2a=6\"$
\n" ); document.write( " $\"a=-3\"$

\n" ); document.write( "ANSWER:

\n" ); document.write( "One form of the polynomial function is $\"f%28x%29=-3%28x-1%29%28x-4%29\"$

\n" ); document.write( "In standard polynomial form that is $\"f%28x%29=-3x%5E2%2B15x-12\"$

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