Class 11Mathematics4-2.Quadratic Equations and InequationsMix Examples-Quadratic Equations and Inequations
DifficultFor $0 < c < b < a$,let $(a+b-2c)x^2 + (b+c-2a)x + (c+a-2b) = 0$ and $\alpha \neq 1$ be one of its roots. 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 $c$.
$(I)$ 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 $c$.
- ABoth $(I)$ and $(II)$ are true
- BNeither $(I)$ nor $(II)$ is true
- COnly $(II)$ is true
- DOnly $(I)$ is true
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