Q. 173.8( 8 Votes )

Find all the zero

Answer :

Let us assume f (x) = 2x4 - 3x3 ‒ 5x2 + 9x - 3

As and – are the zeros of the given polynomial therefore each one of (x - ) and (x + ) is a factor of f (x)


Consequently, (x – ) (x + ) = (x2 – 3) is a factor of f (x)


Now, on dividing f (x) by (x2 – 3) we get:



f (x) = 0


2x2 - 3x2 – 5x2 + 9x - 3 = 0


(x2 – 3) (2x2 – 3x + 1) = 0


(x2 - 3) (2x2 – 2x – x + 1) (2x – 1) (x - 1) = 0


(x – ) (x + ) (2x – 1) (x - 1) = 0


x = or x = - or x = or x = 1


Hence, all the zeros of the given polynomial are , -, and 1


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