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Let a, b,c in R and a ne 0. If alpha is ...

Let a, b,c `in` R and a `ne` 0. If `alpha` is a root of `a^(2) x^(2)` + bx + c = 0 , `beta` is a root of `a^(2) x^(2)` - bx - x = 0 and 0 `lt alpha lt beta`. Then the equation `a^(2) x^(2) + 2 bx ` + 2c = 0 has a root `gamma` that always satisfies :

A

`gamma=(alpha+beta)/(2)`

B

`gamma=alpha+(beta)/(2)`

C

`gamma=(alpha)/(2)+beta`

D

`alpha le gamma le beta`

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The correct Answer is:
A
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