document.write( "Question 384096: say u+iv (where u and v are real numbers, and i is the imaginary unit) is a root of a quadratic polynomial; then, is u-iv also a root of that polynomial? Why, or why not? \n" ); document.write( "

Algebra.Com's Answer #271887 by richard1234(7193) $\"\"$ $\"About$

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Yes. From the quadratic formula, we have\r
\n" ); document.write( "\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28b%5E2+-+4ac%29%29%2F2a\"$ \r
\n" ); document.write( "\n" ); document.write( "Suppose the discriminant was negative. Then, this value x becomes\r
\n" ); document.write( "\n" ); document.write( " $\"%28-b+%2B-+di%29%2F2a+=+%28-b%2F2a%29+%2B-+%28d%2F2a%29i\"$ where d is real. We can assign arbitrary values u and v to obtain\r
\n" ); document.write( "\n" ); document.write( "x = $\"u+%2B-+vi\"$ .\r
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