If the polynomial equation \[{{a}_{n}}{{x}^{n}}+{{a}_{n-1}}{{x}^{n-1}}+.....+{{a}_{2}}{{x}^{2}}+{{a}_{1}}x+{{a}_{0}}=0\],n positive integer, has two different real roots \[\alpha \]and \[\beta \], then between \[\alpha \text{ }and\text{ }\beta \], the equation \[n{{a}_{n}}{{x}^{n-1}}+(n-1){{a}_{n-1}}{{x}^{n-2}}+....+{{a}_{1}}=0\] has

• A. Exactly one root
• B. At most one root
• C. At least one root
• D. No root