Question

4. If two zeroes of the polynomial x4 – 6x2 – 26x² + 138x - 35 are 2 + V3, find other zeroes.
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Answer 1

CORRECT QUESTION.

Two zeroes of the polynomial x^4 - 6x^3 - 26x^2 +138x - 35 are 2+ √3 and 2 - √3

TO FIND ALL THE ZEROES.

EXPLANATION.

zeroes of the polynomial are =

x^4 - 6x^3 - 26x^2 + 138x - 35

Two zeroes are = 2 + √3 and 2 - √3

x = 2 + √3 and x = 2 - √3

x - ( 2 +√3 ) and x - ( 2 - √3 )

x - 2 - √3 and x - 2 + √3

products of both zeroes

(x - 2 - √3)(x - 2 +√3)

( x - 2 )^2 - (√3)^2

x^2 + 4 - 4x - 3

x^2 - 4x + 1

divide the polynomial by x^2 - 4x + 1

we get,

quotient = x^2 - 2x - 35

remainder = 0

factories quotient into middle term split.

x^2 - 2x - 35 = 0

x^2 - 7x + 5x - 35 = 0

x ( x - 7 ) + 5 ( x - 7 ) = 0

( x + 5 ) ( x - 7 ) = 0

x = -5 and x = 7

Therefore,

All zeroes are =

2 + √3, 2 - √3, -5 , 7

NOTE= ALSO SEE THE ATTACHMENT IMAGE