find all the zeros of the polynomial P of X is equals to X ki power 4 - 4 x cube minus 4 x square + 8 x + 7 it is being given that two of its zeros are (3 - √2 ) and (3-√2)
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Let p( x ) = 2x⁴ - 11x³ + 7x² + 13x - 7 ,
It is given that ( 3 + √2 ) and ( 3 - √2 ) are
two zeroes of p( x ).
[ x - ( 3 + √2 ) ] , [ x - ( 3 - √2 ) ] are factors
of p( x ).
Now ,
[ x - ( 3 + √2 ) ] [ x - ( 3 - √2 ) ]
= [ ( x - 3 ) + √2 ] [ ( x - 3 ) - √2 ]
= ( x - 3 )² - ( √2 )²
= x² - 6x + 9 - 2
= x² - 6x + 7 is a factor of p( x )
x² - 6x + 7 ) 2x⁴ -11x³ +7x² + 13x - 7(2x²+x -1
**************2x⁴ -12x³ + 14x²
________________________
********************x³ - 7x² + 13x
********************x³ -6x² + 7x
________________________
***********************-x² + 6x - 7
***********************-x² + 6x - 7
________________________
****************************0
By Division algorithm :
Dividend = quotient × divisor + remainder
p( x ) = ( 2x² + x - 1 ) ( x² - 6x + 7 ) + 0
= [ 2x² + 2x - x - 1 ] ( x² - 6x + 7 )
= [ 2x( x + 1 ) - 1( x + 1 ) ] ( x² - 6x + 7 )
= ( x + 1 )( 2x - 1 )[x - ( 3 + √2 )][ x - ( 3 -√2 )]
Therefore ,
Other two zeroes of p( x ) are
x = - 1 , x = 1/2
If you satisfy on my answer please mark it BRAINLIEST ✏️ ✏️✏️✏️✏️✏️✏️✏️✏️
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Step-by-step explanation:
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