Question

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

Answer 1

EXPLANATION.

• GIVEN

zeroes of the polynomial are =

x^4 + x^3 - 34x^2 - 4x + 120

if two zeroes are = 2 and -2

To Find all the zeroes of the polynomial,

according to the question,

x = 2 and x = -2

x - 2 = 0 and x + 2 = 0

products of the zeroes of polynomial

(x - 2)(x + 2 ) = 0

x^2 - 4

on dividing this polynomial by = x^2 - 4

we get,

x^2 + x - 30

factories the equation in middle term split,

we get,

x^2 + 6x - 5x - 30 = 0

x ( x + 6 ) - 5 ( x + 6 ) = 0

( x - 5 )(x + 6 ) = 0

x = 5 and x = -6

Therefore,

zeroes of polynomial are =

2,-2,5,-6

Note = also see the image attachment.