Application of DerivativeMedium
Question
If the polynomial equation
anxn + an-1 xn-1 + ..... + a2x2 + a1x + a0 = 0
n positive integer, has two different real soots α and β, then between α and β, the equation nanxn-1 + (n - 1)an-1xn-2 + ...... a1 = 0 has in the interval (α, β)
anxn + an-1 xn-1 + ..... + a2x2 + a1x + a0 = 0
n positive integer, has two different real soots α and β, then between α and β, the equation nanxn-1 + (n - 1)an-1xn-2 + ...... a1 = 0 has in the interval (α, β)
Options
A.Exactly one root
B.Atmost one root
C.Atleast one root
D.no root
Solution
anxn + an-1xn-1 + ..... + a2x2 + a1x + a0 = 0
then
nanxn-1 + (n - 1)an-1 xn-2 ...... a1 = 0
has atleast one root
then
nanxn-1 + (n - 1)an-1 xn-2 ...... a1 = 0
has atleast one root
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