If two zeroes of the polynomial 2x⁴–9x³+5x²+3x–1 are 2 + √3 and 2 – √3, find the other zeroes of the polynomial.
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HELLO DEAR,
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
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
InnocentBachiNo1:
thanks :)
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1
Answer:
Hope this helps you ✌️✌️
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