Question

Finding the Roots/Zeros

Answer 1

Answer:

  x = {-√7, √7, -i, i}

Step-by-step 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}