document.write( "Question 1120457: Suppose the product of the roots of a quadratic equation is given, do you think you can determine the equation? Justify your answer.
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Algebra.Com's Answer #736147 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "No; you can't tell what the equation is.

\n" ); document.write( "Suppose the roots are p and q; then the equation is

\n" ); document.write( " $\"%28x-p%29%28x-q%29+=+0\"$
\n" ); document.write( " $\"x%5E2-px-qx%2Bpq+=+0\"$
\n" ); document.write( " $\"x%5E2-%28p%2Bq%29x%2Bpq+=+0\"$

\n" ); document.write( "Now suppose, for example, that you are told that the product of the roots is pq = 20. Then you know the equation is

\n" ); document.write( " $\"x%5E2-%28p%2Bq%29x%2B20+=+0\"$

\n" ); document.write( "where the product of p and q is 20. But there are an infinite number of possibilities for that:

\n" ); document.write( "p, q = 20 and 1: x^2-21x+20 = 0
\n" ); document.write( "p, q = 10 and 2: x^2-12x+20 = 0
\n" ); document.write( "p, q = 5 and 4: x^2-9x+20 = 0
\n" ); document.write( "p, q = -5 and -4: x^2+9x+20 = 0
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\n" ); document.write( "And those are only some of the possibilities where the roots are integers.... \n" ); document.write( "

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