jee-main 2024 Q62

jee-main · India · session1_31jan_shift1 Solving quadratics and applications Finding a ratio or relationship between variables from an equation

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 $c$.
(1) Both (I) and (II) are true
(2) Neither (I) nor (II) is true
(3) Only (II) is true
(4) Only (I) is true

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 $c$.\\
(1) Both (I) and (II) are true\\
(2) Neither (I) nor (II) is true\\
(3) Only (II) is true\\
(4) Only (I) is true

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