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If \(a, b, c\) are in Arithmetic Progression (AP), then the roots of the equation \(a x^2-2 b x+c=0\) are
Options:
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2846 Upvotes
Verified Answer
The correct answer is:
\(1, \frac{c}{a}\)
Given, \(a, b, c\) are in AP
\(\begin{aligned}
2 b & =a+c \\
a x^2-2 b x+c & =0 \\
a x^2-(a+c) x+c & =0 \\
a x^2-a x-c x+c & =0 \\
a x(x-1)-c(x-1) & =0 \\
(x-1)(a x-c) & =0 \\
x & =1, \frac{\mathrm{c}}{\mathrm{a}}
\end{aligned}\)
Hence, option (a) is correct.
\(\begin{aligned}
2 b & =a+c \\
a x^2-2 b x+c & =0 \\
a x^2-(a+c) x+c & =0 \\
a x^2-a x-c x+c & =0 \\
a x(x-1)-c(x-1) & =0 \\
(x-1)(a x-c) & =0 \\
x & =1, \frac{\mathrm{c}}{\mathrm{a}}
\end{aligned}\)
Hence, option (a) is correct.
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