Question

find all the zeroes of the polynomial x4-3x3-6x-4 if two zeroes are root 2 and - root 2​

Answer 1

Answer:

Step-by-step explanation:

by the way it is + 6x and not - 6x.

Answer 2

Answer:

All zeroes are √2 , -√2 , 1 and 2.

Step-by-step explanation:

Given: Zeroes of the polynomial $x^4-3x^3+6x-4$ is  √2 and -√2

To find: All zeroes of the given polynomial.

let , $p(x)=x^4-3x^3+6x-4$

From the given zeroes and using factor theorem,

( x - √2 ) and ( x + √2 ) are the factors of p(x)

⇒ x² - 2 is a factor of p(x)

Now, on dividing p(x) with x² - 2

we get,

p(x) = ( x² - 2 )( x² - 3x + 2 )

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

      = ( x - √2 )( x + √2 ) [ x ( x - 2 ) - ( x - 2 ) ]

      = ( x - √2 )( x + √2 )( x - 2 )( x - 1 )

Therefore, All zeroes are √2 , -√2 , 1 and 2.