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Find a quadratic with real coefficients and quadratic term $x^{2}$ that has $5-4 i$ as a root.
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If $5-4 i$ is a root, then so is $5+4 i$. The sum of the roots is $5-4 i+5+4 i=10$, and the product of the roots is $(5-4 i)(5+4 i)=25+16=41$. The quadratic is
$x^{2}-10 x+41$
Final Answer: The final answer is $x^{2}-10 x+41$
by Platinum (147,718 points)

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