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

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

`gamma =alpha//4+beta`

`beta lt gamma`

`gamma = alpha //2 +beta`

`alpha lt gamma lt beta`

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