Question

find all the zeros of 2 x to the power 4- 3 x to the power 3 minus 3 x to the power 2 + 6 x minus 2 if you know that two of its zeros are root 2 and minus root 2​

Answer 1

Answer:

Since two roots of polynomial are given so we can write root like this

(X-under root 2)(X+under root 2)

By multiplying roots we get

X^2-2

Now devide the polynomial with x^2-2

After dividing we get quotient as 2x^2-3x+1

Now factorise 2x^2-3x+1

2x^2-2x-1x+1

2x(x-1)-1(x+1)

(2x-1)(x-1)

Therefore

2x-1=0

X=1/2

2. X-1=0

X=1

So all the zeros of polynomial are root 2, - root 2,1/2and 1