Trig quadratic equation

if a quadratic has more than 2 roots , then the equation must be identicaly zero .

i.e. the coeff. of x² = coeff. of x = constant =0

applying this concept twice ,

we have , a=sinθ , b=0 ,c = -cosθ

a+b+c =1

hence sinθ - cosθ =1

θ = π/2 ,π

if any (so called)quadratic eqn has more than 2 roots it must be an identity na..??