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

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

A

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

B

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

C

`gamma =alpha`

D

`alpha lt gamma lt beta `

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The correct Answer is:
D
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