If α and β are the roots of the equation x 2 + px + q = 0 and also x 3900 + p 1950 x 1950 + q 1950 = 0 and if 
, 
are the roots of the x n + 1 + (x + 1) n = 0 then the value of n must be equal to…………..
Text Solution
Verified by Experts1950
(1950)
Sol. x 2 + px + q = 0 roots ( α , β )
α + β = − p, αβ = q
Also ( α , β ) are the of the roots equation
x 3900 + p 1950 x 1950 + q 1950 = 0
∴ α 1950 + β 1950 = – p 1950 and α 1950 β 1950 = q 1950 …(1)
Now α/β is a root of x n + 1 + (x + 1) n = 0
+ 1 + 
= 0
α n + β n + ( α + β ) n = 0
α n + β n + (– p) n = 0 ⇒ α n + β n = – (–p) n ….(2)
from (1) and (2)
n = 1950
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