First slide

Theory of equations

Question

The roots of the equation $x^{3} - 3 x - 2 = 0$ are

Easy

A

$- 1, - 1, 2$
B

$- 1, 1, - 2$
C

$- 1, 2, - 3$
D

$- 1, - 1, - 2$

Solution

clearly -1 is a root of the given equation and -1 is also root of
$f^{'} (x) = 3 x^{2} - 3 = 0, h e n c e - 1 i s c o m m o n r o o t o f t h e e q u a t i o n s f (x) = 0 a n d f^{'} (x) = 0 . ∴ - 1 i s t h e r e p e a t e d r o o t . \sin c e S_{1} = 0 \Rightarrow t h i r d r o o t = 2$
roots are -1,-1,2

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