Question

find all the zeros of the polynomial x cube + 3 x square - 2 x - 6 if two of its zeros are root 2 - root 2

Answer 1

Hi ,

Let p( x ) = x³ + 3x² - 2x - 6

It is given that √2 , -√2 are the two zeros

of p( x ).

( x - √2 ) , ( x + √2 ) are two factors of p( x ),

( x - √2 )( x + √2 ) = x² - ( √2 )² = x² - 2 is

also a factor of p( x ).

x² - 2 ) x³ + 3x² - 2x - 6 ( x + 3
*********x³ + 0 - 2x
_________________
**************3x² + 0 - 6
**************3x² + 0 - 6
___________________
*******************0

By division algorithm :

dividend = quotient × divisor + remainder

p( x ) = ( x + 3 )(x² - 2 )

= ( x + 3 ) ( x + √2 )( x - √2 )

Therefore ,

x + 3 is a factor of p( x ) .

- 3 , √2 , - √2 is a factors of p( x ).

I hope this helps you.

: )

Answer 2

Answer:

Step-by-step explanation: