Q86 / 160 · AP EAMCET 2020 (18 Sep Shift 2) · Mathematics

If \(a, b, c\) are in Arithmetic Progression (AP), then the roots of the equation \(a x^2-2 b x+c=0\) are

  • Correct answer
    A
    \(1, \frac{c}{a}\)
  • B
    \(\frac{-1}{a},-c\)
  • C
    \(-1, \frac{-c}{a}\)
  • D
    \(-2, \frac{-c}{2 a}\)

Solution

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.

Hence, the correct answer is option: 'A'.

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