Question

(6) Find all the zeros of 2x -3x³-3x² + 6x-2 if two zeroes are √2 and −
2
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Answer 1

Given ,

✓2 and -✓2 are the zeroes of given polynomial

Now ,

( x + ✓2 ) ( x - ✓2 ) = x² - 2

Now ,

by long division method

x - 2 | -3x³ - 3x²+ 8x - 2 | -3x²-3x + 2

| -3x³ + 6x

-----------------------------

-3x² + 2x - 2

- 3x² +6

---------------------------

2x + 4

2x - 4

----------------

x

now ,

other zeroes are : -3x² - 3x + 2

- 3x² - 6x + 3x + 2

- 3x( x + 2) + 1(3x+2)

(- 3x + 1 ) ( 3x + 2 )

Hence , 1/3 and - 2/3 are required zeroes .