Question

Find all the zeroes of a polynomial x4+x3-34x2-4x+120 if two of its zeroes are 2 and -2

Answer 1

Hey there !!
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Since two zeroes are 2 and –2.
x = 2 or x = –2
=> ( x – 2 ) ( x + 2 ) = 0
=> x² – 4
So, x² – 4 is a factor of given polynomial.

Refer to the attachment for division.

Now, x² + x – 30 = 0
x² + 6x – 5x – 30 = 0
x ( x + 6 ) – 5 ( x + 6 ) = 0
( x – 5 ) ( x + 6 ) = 0
( x – 5 ) = 0 or ( x + 6 ) = 0
x = 5 of x = –6

Thus, the zeroes of x⁴ + x³ – 34x² – 4x + 120 are 2, –2, 5 and –6.
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Hope my ans.'s satisfactory. (^-^)

Answer 2

Answer:

here is ur attached answer