Mathematics · 2024
JEE Main · 31 January 2024, Shift 1 · Q8
For 0<c<b<a, let (a+b-2 c) x^2+(b+c-2 a) x+(c+a-2 b)=0 and α ≠ 1 be one of its root. Then, among the two statements (I) If α ∈(-1,0), then b cannot…
For $\displaystyle 0<c<b<a$, let $\displaystyle (a+b-2 c) x^2+(b+c-2 a) x+(c+a-2 b)=0$ and $\displaystyle \alpha \neq 1$ be one of its root. Then, among the two statements
(I)
If $\displaystyle \alpha \in(-1,0)$, then $\displaystyle b$ cannot be the geometric mean of $\displaystyle a$ and $\displaystyle c$
(II)
If $\displaystyle \alpha \in(0,1)$, then $\displaystyle b$ may be the geometric mean of $\displaystyle a$ and $\displaystyle c$
Official answer
From NTA’s final answer key for this paper.
(3)
Both (I) and (II) are true
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JEE Main 2024 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.