AP EAMCET · Maths · Quadratic Equation
If \(a, b, c\) are in Arithmetic Progression (AP), then the roots of the equation \(a x^2-2 b x+c=0\) are
- A \(1, \frac{c}{a}\)
- B \(\frac{-1}{a},-c\)
- C \(-1, \frac{-c}{a}\)
- D \(-2, \frac{-c}{2 a}\)
Answer & Solution
Correct Answer
(A) \(1, \frac{c}{a}\)
Step-by-step Solution
Detailed explanation
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.
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