If sec `alpha and alpha` are the roots of `x^2-p x+q=0,` then (a) `p^2=q(q-2)` (b) `p^2=q(q+2)` (c)`p^2q^2=2q` (d) none of these

Explanation

a)`p^2=alpha^2+secc^2alpha+2alphasecalpha`

`q(q-2)=alphasecalpha(alphasecalpha-2)`

`=alpha^2sec^2alpha-2alphasecalpha`

`p^2!=q(q-2)`

b)`q(q+2)=alpha^2sec^2alpha+2alphasecalpha!=(alpha+secalpha)^2`

c)`p^2q^2=(alpha^2+sec^2alpha+2alphasecalpha)(alpha^2sec^2alpha)`

`=alpha^4secc^4alpha+alpha^2secc^4alpha+2alpha^3sec^3alpha`

`2q=2alphasecalpha`

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