If `cos^(4)theta+p, sin^(4)theta+p` are the roots of the equation `x^(2)+a(2x+1)=0` and `cos^(2)theta+q,sin^(2)theta+q` are the roots of the equation `x^(2)+4x+2=0` then a is equal to

Options

A. -2
B. -1
C. 1
D. 2

Explanation

`:'cos^(4) theta-sin^(4)theta=cos 2 theta`
`impliescos^(4)theta-sin^(4) theta=cos^(2)theta-sin^(2) theta`
`implies(cos^(4) theta+p)-(sin^(4) theta+p)=(cos^(2)theta+q)-(sin^(2)theta+q)`
`implies(sqrt(4a^(2)-4a))/1=(sqrt(16-8)/1[ :' alpha-beta=(sqrt(D))/a]`
`implies4a^(2)-4a=8` or `a^(2)-a-2=0`
or `(a-2)(a+1)=0` or `a=2,-1`