For 0< {\c}< {\b}< {\a}, let ( {\a}+ {\b}-2 {\c}) {\x}^2+( {\b}+ {\c}-2 {\a}) {\x} +( {\c}+ {\a}-2 {\b})=0 and \alpha \neq 1 be one of its root. Then, among the two statements (I) If \alpha \in(-1,0), then b cannot be the geometric mean of {\a} and {\c} (II) If \alpha \in(0,1), then {\b} may be the geometric mean of {\a} and {\c} [31-Jan-2024 Shift 1]

Correct Answer is : Both (I) and (II) are true

JEE Main 31-Jan-2024 Shift 1 Solved Paper

Section: Mathematics

Question : 1 of 90

Marks: +1, -0

For 0<c<b<a, let (a+b−2c)x2+(b+c−2a)x +(c+a−2b)=0 and α≠1 be one of its root. Then, among the two statements
(I) If α∈(−1,0), then b cannot be the geometric mean of a and c
(II) If α∈(0,1), then b may be the geometric mean of a and c

[31-Jan-2024 Shift 1]

Both (I) and (II) are true
Neither (I) nor (II) is true
Only (II) is true
Only (I) is true

Validate

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