Given that√2 is the root of cubic polynomial 6x3 + 2x2-10x -4√2 find the other two roots

Answer 1

a little synthetic division shows that (x-√2) does not divide the cubic.

In fact f(√2) = 4-2√2

Check for typos and try again.

Once you have done the division, you will be left with a quadratic, which you can then solve in the usual way.

Answer 2

f(x)=6x3+√2x2-10x-4√2
Since x=√2 is a zero of f(x)
=>(x-√2) is a factor of f(x)
x-√2)6x3+√2x2-10x-4√2(6x2+7√2x+4
6x3-6√2x2
-------------------
7√2x2-10x-4√2
7√2x2-14x
-----------------
4x-4√2
4x-4√2
-------------
O
Now, 6x2+7√2x+4=0
=> 6x2+4√2x+3√2x+4=0
=> 2x(3x+2√2)+√2(3x+2√2)=0
=> (3x+2√2)(2x+√2)=0
=> 3x+2√2=0 or 2x+√2=0
=> x=-2√2/3 or x=-√2/2