GATE EC 2013 (Set 2) Question 7: Polynomial Roots - Analyzing f(x) = a₄x⁴ + a₃x³ + a₂x² + a₁x - a₀

Consider p(s)=s3+a2s2+a1s+a0 with all real coefficients. It is known that its derivative p'(s) has no real roots. The number of real roots of p(s) is

A polynomial f(x) = a4x4 + a3x3 + a2x2 + a1x − a0 with all coefficients positive has

A polynomial f(x) = a4x4 + a3x3 + a2x2 + a1x - a0 with all coefficients positive has