Question

find all the zeroes of 2x^4 - 9x³+5x²+3x-1 if two of it zeroes are (2+√3) and (2-√3).

Answer 1

Answer:

given that:-

x=(2+√3) and ,X=(2-√3)

now ,

{(x-2)-√3} × {(x-2)+√3}

hence, 

{ x -(2 -√3)}{x -(2+√3)} is a factor of given polynomial . 

{ x² -(2+√3)x -(2-√3)x +(2-√3)(2+√3)} is a factor of given polynomial .

{ x²-(4)x + 1} is a factor of given polynomial .

hence, x²-4x +1 is divisible by given polynomial .

now, 

x² -4x +1 ) 2x⁴ -9x³+ 5x² +3x -1( 2x²-x -1

2x⁴ -8x³ +2x² 

_______________

-x³ +3x² +3x 

-x³ +4x² -x

______________

-x² + 4x -1 

-x² +4x -1 

____________

0000

Then,

( 2x² -x -1) is a factor of the two polynomial

 

now, 

2x² -x -1 =0

2x² -2x +x -1 =0

2x( x -1)+ ( x -1) = 0

(2x +1)( x -1)=0

x = -1/2 and 1 

So,

-1/2 and 1 are two roots of given polynomial .

Answer 2

Answer:

Hope this helps you ✌️✌️