Q. 144.4( 18 Votes )

If 3 and ‒3 are t

Answer :

Let us assume f (x) = x4 + x3 ‒ 11x2 ‒ 9x + 18

As 3 and – 3 are the zeros of the given polynomial therefore each one of (x + 3) and (x - 3) is a factor of f (x)


Consequently, (x – 3) (x + 3) = (x2 – 9) is a factor of f (x)


Now, on dividing f (x) by (x2 – 9) we get:



f (x) = 0


(x2 + x – 2) (x2 – 9) = 0


(x – 1) (x + 2) (x – 3) (x + 3) = 0


x = 1 or x = - 2 or x = 3 or x = - 3


Hence, all the zeros of the given polynomial are 1, -2, 3 and -3


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