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Let p ,q be real numbers . If alpha" is ...

Let p ,q be real numbers . If `alpha"` is a root of `x^(2)+3p^(2)x+5q^(2)=0,beta" is a root of "x^(2)+9p^(2)+15q^(2)=0and0ltalphaltbeta" then the equation" x^(2)+6p^(2)+10q^(2)=0` has a root `gamma` that always satisfies -

A

`gamma=(alpha)/(4)+beta`

B

`betaltgamma`

C

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

D

`alphaltgammaltbeta`

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The correct Answer is:
D
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