If unity is double repeated root of then
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I t i s g i v e n t h a t p x 3 + q ( x 2 + x ) + r h a s 1 a s t w i c e r e p e a t e d r o o t . . . . . . s o , l e t t h e e x p r e s s i o n a b o v e b e f ( x ) . f ′ ( x ) = 3 p x 2 + 2 q x + q . . . f ′ ( 1 ) = 0 ⋆ { ∵ , f ( x ) h a s 1 a s t w i c e r e p e a t e d r o o t . H e n c e 1 i s o n l y r o o t o f f ′ ( x ) } → 3 p + 3 q = 0 ⇒ p = − q H e n c e , p q < 0