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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

A

`-(pi)/(4)`

B

`(pi)/(4)`

C

`(3pi)/(4)`

D

`-(3pi)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
`sqrt(5-12i) = sqrt((3-2i)^(2)) = pm (3-2i)`
`sqrt(-5-12i)= sqrt((2-3i)^(2)) = pm (2-3i)`
`rArr z = sqrt(5-12i) + sqrt(5-12i) = sqrt((3-2i)^(2)) = pm (3-2i)`
`sqrt(-5-12i)= sqrt((2-3i)^(2)) = pm (2-3i)`
`rArr z = sqrt(5-12i) + sqrt(-5-12i)`
`=- 1-i, -5 + 5i,5-5i, 1+i`
Therefore, principal values of arg are `- 3pi//4, 3pi//4,-pi//4, pi//4`.
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