Question

x=1 x=-1 are zeros of polynomial ax^3+x^2-2x+b find value of a&b

Answer 1

$\textbf{Hello user !! }$

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a x^3 + x^2 - 2x + b

Put the value of x in the given polynomial !

p ( 1 ) = a ( 1 ) + ( 1 )^2 - 2 ( 1 ) + b

p ( 1 ) = a + 1 - 2 + b

p ( 1 ) = a - 1 + b

a + b = 1 _____1st equation

p ( - 1 ) = a ( - 1 ) + ( - 1 ) ^2 - 2 ( - 1 ) + b

p ( - 1 ) = - a + 1 + 2 + b

p ( - 1 ) = - a + 3 + b

- a + b = - 3 ___ 2nd equation

Subtracting 2nd equation from 1st equation we will get :-

2 b = 4

b = 4 / 2

b = 2

Put value of b in 1st equation !

a + 2 = 1

a = 1 - 2

a = - 1

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