Question

If + + +...+ + an = 0, then the equation a0xn + a1xn–1 + ...+ an–1x + an = 0 has, in the interval (0, 1),

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

Answer 1

Answer: (B)

At least one root

Answer 2

Equation a_­0xⁿ + a₁x^n–1 +..... + a_{n – 1} x + a_n= 0

f(x) = + $\frac { a _ { 1 } x ^ { n } } { n }$ + ...... + $\frac { a _ { n - 1 } x ^ { 2 } } { 2 }$ + a_nx

f(0) = 0, f(1) = $\frac { \mathrm { a } _ { 0 } } { \mathrm { n } + 1 }$ + + .... + +a_n = 0

 (0, 1) has at least one root of equation