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Alenkasestr [34]
3 years ago
6

Find a polynomial with integer coefficients that satisfies the given conditions.

Mathematics
1 answer:
stepladder [879]3 years ago
8 0
\bf \textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad 
a^2-b^2 = (a-b)(a+b)
\\\\\\
\textit{also recall that }~~~i^2=-1\\\\
-------------------------------\\\\
\begin{cases}
x=5+i\implies &x-5-i=0\\
x=5-i\implies &x-5+i=0
\end{cases}
\\\\\\
(x-5-i)(x-5+i)=\stackrel{\textit{original polynomial}}{0}
\\\\\\\
[(x-5)~~-~~i]~[(x-5)~~+~~i]=0\implies [(x-5)^2~~-~~i^2]=0
\\\\\\
(x^2-10x+25)~~-~~(-1)=0\implies x^2-10x+25+1=y
\\\\\\
x^2-10x+26=y
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Find out the how much fluid should be drained and replaced with pure antifreeze so that the new mixture is 60% antifreeze .

To proof

let us assume that the fluid should be drained and replaced with pure antifreeze be x .

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