Q.
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
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a
2
b
-1
c
-2
d
1
answer is A.
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Detailed Solution
We have, cos2θ−sin2θ=cos2θ⇒ cos4θ−sin4θ=cos2θ⇒ (−2b)2−4b=(−4)2−4×2(since L.H.S. is difference of roots of first equation and R.H.S. is difference of roots of second equation)or 4b2−4b=16−8=8or 4b2−4b−8=0or b2−b−2=0or (b+1)(b−2)=0or b=2,−1
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