Question

find all the zeros of 2 x power 4 - 3 x cube minus 3 X square + 6 X + 2 if two zeros are under root 2 and minus under root 2​

Answer 1

Given:

2 x power 4 - 3 x cube minus 3 X square + 6 X - 2 = 0

The correct question is given here.

To Find:

All the zeros of 2 x power 4 - 3 x cube minus 3 X square + 6 X - 2 if two zeros are under root 2 and minus under root 2​.

Solution:

Given two of the zeros are

• x = √2 and x = -√2
• Therefore, x - √2 = 0 and x + √2 = 0
• Therefore, ( x - √2)( x + √2)=0
• x² - 2 = 0

Now lets divide P(x) =  2$x^{4}$ - 3$x^{3}$ - 3$x^{2}$ + 6x - 2 by g(x) =  x² -2

Therfore ,

quotient = 2x² - 3x + 1

Solving,

• 2x² - 3x + 1 = 0
• 2x² -2x -x + 1 = 0
• 2x(x - 1) -1 ( x -1 ) = 0
• x =1  and x =1/2

Therefore

All the zeroes of 2 x power 4 - 3 x cube minus 3 X square + 6 X - 2 if two zeros are under √2 , - √2 , 1 and 1/2.​

Answer 2

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