The equation sin4x+asin2x+1=0  will have a solution if a  belongs to

The equation sin4x+asin2x+1=0 Let u=sin2x , then u∈[0, 1] ∴  u2+au+1=0  should have at least one solution in [0,  1] ∴  discriminant=a2−4≥0  ⇒a≤−2   or   a≥2 Product of roots=1,  only one root may lie in [0, 1] ∴  f(0)f(1)≤0 ⇒a+2≤0⇒a≤−2 Hence a∈(−∞,  −2]