Adefinite integral of f(x)dx on the interval a to b probably shouldn't be used:

= cos( -x ) * [ - sin( - x ) ] = cosx * sinx ;
cosx * sin x is the right answer !

Answer to your question: a. the fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. the roots are ​ x=1±i7√2 .number of roots=degree of polynomialhere, degree of polynomial is 2 so number of roots will be 2.hope it *_*