Question

obtain all the zeroes...........

Answer 1

hence , zeroes are √2 and -√2
( x - √2)(x+√2)
= x²-(√2)²
= x²-2
so, x²-2 is a factor

2x² - 3x + 1
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x²-1 [ 2x⁴-3x³-3x²+6x-2 ]

2x⁴ - 4x²

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- 3x³+x²+6x -2

- 3x³ + 6x

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x² - 2

x² - 2

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null

so,

2x⁴ - 3x³ - 3x² + 6x - 2 = ( x²-2)(2x²-3x+1).
= (x² - 2)(2x²-(2+1)x+1)

= (x²-2) ( 2x²-2x-x+1 )

= (x²-2) {(2x(x -1)-1(x-1) }

= (x²-2) ( 2x-1)(x-1)

so others zeroes should be

2x-1= 0 or, x = 1
=> x = 1/2


All zeroes are √2,-√2,1/2 and 1
thanks

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