First slide
Theory of equations

If cos4θ+α and sin4θ+α are the roots of the equation x2+2bx+b=0 and cos2θ+β,sin2θ+β are the roots of the equation  x2+4x+2=0, then values of b are


We have, cos2θsin2θ=cos2θ

 cos4θsin4θ=cos2θ (2b)24b=(4)24×2

(since L.H.S. is difference of roots of first equation and R.H.S. is difference of roots of second equation)

or   4b24b=168=8or   4b24b8=0or   b2b2=0or   (b+1)(b2)=0or   b=2,1

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