Find all zeroes of the polynomial $({2 x}^{4} - 9 x^{3} + {5 x}^{2} + 3 x - 1)$ if two of its zeroes are $(2 + \sqrt{3}) a n d (2 - \sqrt{3}) .$

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Solution

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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Similar questions

2 + \sqrt{3} and 2 - \sqrt{3}

(2 x^{4} - 9 x^{3} + 5 x^{2} + 3 x - 1)

(2 + \sqrt{3})

(2 - \sqrt{3})

2 x^{4} - 9 x^{3} + 5 x^{2} + 3 x - 1

2 + \sqrt{3}

2 - \sqrt{3}

2 x^{4} - 11 x^{3} + 7 x^{2} + 13 x - 7

(3 + \sqrt{2})

(3 - \sqrt{2}) .

p (x) = 2 x^{4} - 9 x^{3} + 5 x^{2} + 3 x - 1

2 + \sqrt{3}

2 - \sqrt{3}

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