Question

Find all zero of the polynomial (2x4-9x3+5x2+3x-1)if two of its zero are (2+√3)and(2-√3)

Answer 1

x = 2 + √3 and x = 2 - √3 are Zeros of p ( x )

( x - 2 - √3 ) ( x - 2 + √3 )

( using identity ( a - b ) ( a +b ) = a² - b²

then,

( x - 2 )² - ( √3 )²

x² + 4 - 4x - 3

x² + 1 - 4x .... ( i )

When we divide p ( x ) by ( i ) we get the other zeros

Other zeros are :- x = 1 and x = -1/2

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Answer 2

x = 2+root 3
x = 2 - root 3

(x - (+root 3) (x -(-root 3)

(x - root 3)(x + root 3)
x^2 - 4x + 1

2x^4 - 9x^3 + 5x^2 + 3x - 1 / x^2 - 4x + 1

we get 2x^2 - x -1
2x^2 - 2x + x - 1
2x( x - 1 ) + 1 (x -1)
(2x +1) (x-1)
2x + 1 = 0
x-1 =0
x = -1/2
x = 1

So the zeroes of polynomial is (2 + root 3), (2- root3) , -1/2 , 1