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If one of the roots of the equation $a(b-c) x^{2}+b(c-a) x+$ $c(a-b)=0$ is 1, what is the second root?
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Verified Answer
The correct answer is:
$\frac{c(a-b)}{a(b-c)}$
Givenequation is
$a(b-c) x^{2}+b(c-a) x+o(a-b)=0$
Let $\alpha$ be the second root.
$\mathrm{So},(\alpha)(1)=\frac{c(a-b)}{a(b-c)}$
Hence, $\alpha=$ second root $=\frac{c(a-b)}{a(b-c)}$
$a(b-c) x^{2}+b(c-a) x+o(a-b)=0$
Let $\alpha$ be the second root.
$\mathrm{So},(\alpha)(1)=\frac{c(a-b)}{a(b-c)}$
Hence, $\alpha=$ second root $=\frac{c(a-b)}{a(b-c)}$
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