document.write( "Question 223003: What would the quadratic eqation be with the roots 2/3 and 4. i got this question on a test and i didnt know how to do it can someone help please? \n" ); document.write( "

Algebra.Com's Answer #166857 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
The key to this and similar problems is to understand that if some number, let's call it \"r\", is a root of a polynomial, let's call it P(x), then (x-r) is a factor of P(x) (and vice versa).

\n" ); document.write( "So a polynomial with roots of 2/3 and 4 would be:
\n" ); document.write( " $\"P%28x%29+=+%28x+-+2%2F3%29%28x-4%29\"$
\n" ); document.write( "Multiplying this out we get:
\n" ); document.write( " $\"P%28x%29+=+x%5E2+-4x+-+%282%2F3%29x+%2B+8%2F3\"$
\n" ); document.write( "Adding like terms we get:
\n" ); document.write( " $\"P%28x%29+=+x%5E2+-+%2814%2F3%29x+%2B+8%2F3\"$
\n" ); document.write( "So our quadratic equation is:
\n" ); document.write( " $\"x%5E2+-+%2814%2F3%29x+%2B+8%2F3+=+0\"$
\n" ); document.write( "If we don't want fractions, multiply both sides by 3:
\n" ); document.write( " $\"3x%5E2+-+14x+%2B+8+=+0+\"$
\n" ); document.write( " \n" ); document.write( "

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