Both circle a and circle b have a central angle measuring 140°. the ratio of the radius of circle a to the radius of circle b is 2/3. if the length of the intercepted arc for circle a is 3/4π, what is the length of the intercepted arc for circle b?

The arc length is:
 S = R * theta
 Where,
 R: Radio
 Theta: central angle
 Substituting values we have:
 Circle A:
 Sa = Ra * (140/360) * 2π
 Circle B:
 Sb = Rb * (140/360) * 2π
 The relationship of arcs is:
 Sa / Sb = (Ra * (140/360) * 2π) / (Rb * (140/360) * 2π)
 Rewriting:
 Sa / Sb = (Ra / Rb)
 Substituting values:
 (3 / 4π) / Sb = 2/3
 Clearing Sb
 Sb = (3/2) (3 / 4π)
 Sb = (9 / 8π)
 
 The length of the intercepted arc for circle B is:
 Sb = (9 / 8π)

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 *_*