Answer:
x = {-√7, √7, -i, i}
Explanation:
The quartic can be factored as the product of two quadratics:
f(x) = x^4 -6x^2 -7
f(x) = (x^2 -7)(x^2 +1)
Each quadratic can be factored according to the factoring of the difference of squares:
x^2 -a^2 = (x -a)(x +a)
Of course, the square root of a negative number is imaginary. The full factorization is then ...
f(x) = (x -√7)(x +√7)(x -i)(x +i)
The zeros are ...
x = {-√7, √7, -i, i}