document.write( "Question 382761: Find two numbers such that their sum is 10 and their product is 22? \n" ); document.write( "

Algebra.Com's Answer #271177 by richard1234(7193) $\"\"$ $\"About$

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Let p, q be two roots of a monic quadratic polynomial $\"x%5E2+%2B+bx+%2B+c+=+0\"$ (without loss of generality assume the x^2 coefficient 1).\r
\n" ); document.write( "\n" ); document.write( "By Vieta's formulas, the sum of the roots is -b, and p + q = -b, so b = -10. Also, the product of the roots is c, i.e. pq = 22 --> c = 22. Therefore we have established our polynomial\r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2+-+10x+%2B+22+=+0\"$ which we can find the roots p, q. By the quadratic formula,\r
\n" ); document.write( "\n" ); document.write( "p, q = $\"%2810+%2B-+sqrt%2812%29%29%2F2+=+5+%2B-+sqrt%283%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Therefore the two numbers are $\"5+%2B+sqrt%283%29\"$ and $\"5+-+sqrt%283%29\"$ . \n" ); document.write( "

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