Q. 154.0( 11 Votes )

If 2 and ‒2 are t

Answer :

Let us assume f (x) = x4 + x3 ‒ 34x2 ‒ 4x + 120

As 2 and – 2 are the zeros of the given polynomial therefore each one of (x - 2) and (x + 2) is a factor of f (x)


Consequently, (x – 2) (x + 2) = (x2 – 4) is a factor of f (x)


Now, on dividing f (x) by (x2 – 4) we get:



f (x) = 0


(x2 + x – 30) (x2 – 4) = 0


(x2 + 6x – 5x – 30) (x – 2) (x + 2)


[x (x + 6) – 5 (x + 6)] (x – 2) (x + 2)


(x – 5) (x + 6) (x – 2) (x + 2) = 0


x = 5 or x = - 6 or x = 2 or x = - 2


Hence, all the zeros of the given polynomial are 2, -2, 5 and -6

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