Question

find all the zeros of the polynomial f(x)=2x²-3x²-6x-2 if two of its zero are √2 and -√2​

Answer 1

Since 2 zeros are √2 and-√2, (x-√2)(x+√2)=x^2 -2 is a factor of given polynomial. Now, we divide the given polynomial by x^2-2.

We get, 2x^2-3x+1

Then factorise the 2x^2 -3x+1

So we get, (2x-1)(x-1)

So it's zero are given by x=1/2 and x=1.

Therefore, the zeros of given polynomial are √2,-√2,1/2 and 1.