Question

pls answer this question for me
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Answer 1

Hey Friend ☺

2x^4 - 9x^3 + 5x^2 + 3x - 1 = 0

》2x^4 - 2x^3 - 7x^3 + 5x^2 + 3x - 1 = 0

》2x^3 ( x - 1 ) - 7x^3 + 5x^2 + 3x - 1 = 0

》2x^3 ( x - 1 ) - 7x^3 + 7x^2 - 2x^2 + 3x - 1 = 0

》2x^3 ( x - 1 ) - 7x^2 ( x - 1 ) - 2x^2 + 3x - 1 = 0

》2x^3 ( x - 1 ) - 7x^2 ( x - 1 ) - 2x^2 + 2x + x - 1 = 0

》2x^3 ( x - 1 ) - 7x^2 ( x - 1 ) - 2x ( x - 1 ) + x - 1 = 0

》2x^3 ( x - 1 ) - 7x^2 ( x - 1 ) - 2x ( x - 1 ) + 1 ( x - 1 ) = 0

》( x - 1 )( 2x^3 - 7x^2 - 2x + 1 ) = 0

》( x - 1 )( 2x^3 + x^2 - 8x^2 - 2x + 1 ) = 0

》( x - 1 )[ x^2 ( 2x + 1 ) - 8x^2 - 2x + 1 ] = 0

》( x - 1 )[ x^2 ( 2x + 1 ) - 8x^2 - 4x + 2x + 1 ] = 0

》( x - 1 )[ x^2 ( 2x + 1 ) - 4x ( 2x + 1 ) + 2x + 1 ] = 0

》( x - 1 )[ x^2 ( 2x + 1 ) - 4x ( 2x + 1 ) + 1 ( 2x + 1 ) ] = 0 .

》( x - 1 )( 2x + 1 )( x^2 - 4x + 1 )

So other two required zeroes are 1 & - 1/2

Hope it helps you ..!!

✌

Answer 2

HELLO DEAR,

Brainly source, https://brainly.in/question/2452283

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 .

I hope its help you dear,
Thanks