document.write( "Question 176614: Find a quadratic equation with roots (4+i) and (4-i) \n" ); document.write( "

Algebra.Com's Answer #131689 by solver91311(24713) $\"\"$ $\"About$

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If $\"x+=+4+%2B+i\"$ then $\"x+-+%284+%2B+i%29\"$ is a factor of the quadratic. Similarly, $\"x+-+%284+-+i%29\"$ is a factor of the quadratic and we can say:\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x+-+%284+%2B+i%29%29%28x+-+%284+-+i%29%29+=+0\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Just multiply the two factors to get back to the original quadratic. Hints: Treat these two factors as binomials with $\"x\"$ being one term and $\"4+%2B-+i\"$ as the other term. Remember that multiplying a conjugate pair results in the difference of two squares, that is: $\"%28a+%2B+b%29%28a+-+b%29+=+a%5E2+-+b%5E2\"$ . Therefore $\"%284+%2B+i%29%284+-+i%29+=+16+-+%28-1%29+=+17\"$ \n" ); document.write( "

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