Question

Find all zeros of quadratic polynomial 2 x power 4 - 11 x cube + 7 x square + 13 x minus 7 if 2 of its zeros are 3 + root 2 and 3 minus root 2

Answer 1

Hi ,

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

I hope this helps you.

: )

Answer 2

1. hope this answer may help you in the exam . If you think it is useful then please mark as brainliest