Question

a cubic polynomial ax3+bx2+cx+d is zero with real co efficient has at most n real roots the value of n is​

Answer 1

Answer:

Since x3+bx2+cx+d=0 is a cubic polynomial equaation, it is continuous on [a,b], where a<b, and differentiable on (a,b). Thus, by Roelle's Theorem, there exists dϵ(a,b) such that

f′(d)=0

3x2+2bx+c=0

Hence, this shows that there exists at least one real root on this cubic equation.