To find all the zeros of f(x)=x^4+6x^2-7 means to find the values of x that make f(x)=0. In other words, it means finding solution of the equation x^4+6x^2-7=0 and for this we should factorize x^4+6x^2-7.
For this, let us split middle term in to two components 7x^2 and -x^2. Then x^4+6x^2-7=0 becomes
x^4+7x^2-x^2-7=0 i.e. x^2(x^2+7)-1((x^2+7)=0 or
(x^2-1)(x^2+7)=0. Note that (x^2-1) can be further factorized into (x+1)(x-1). Hence, x^4+6x^2-7=0 can be written as
(x-1)(x+1)(x^2+7)=0 and hence
Rational zeros of f(x) are {-1,1}.
Further if we include complex numbers in domain of x, from (x^2+7)=0, we get (x-isqrt7)(x+isqrt7) or x={isqrt7,-isqrt7}
