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Sameedha Andra
Asked: 2022-11-11T18:17:40+05:30 In:

If `alpha, beta` are the roots of ` a x^2 + bx + c = 0` and `k in R` then the condition so that `alpha < k < beta` is :
A. `ak^(2) + bk + c lt 0`
B. `a^(2) k^(2)+ abk + ac lt 0`
C. `a^(2)k^(2) + abk + ac gt 0`
D. none of these

If `alpha, beta` are the roots of ` a x^2 + bx + c = 0` and `k in R` then the condition so that `alpha < k < beta` is :
A. `ak^(2) + bk + c lt 0`
B. `a^(2) k^(2)+ abk + ac lt 0`
C. `a^(2)k^(2) + abk + ac gt 0`
D. none of these
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  1. Correct Answer – B
    Let `f(x) = ax^(2) + bx + c`. It is given that `alpha, beta` are real roots of `f(x) = 0`. So, k lies between `alpha and beta`, if
    `a f(k) lt 0 rArr a (ak^(2) + bk + c) lt 0 rArr a^(2) k^(2) + abk + ac lt 0`

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