t4 + 4t2 + 4 = 0. Find the roots of the given equation

This equation is a quadratic equation in the form of t^2. We can solve it by using the formula for the roots of a quadratic equation, which is:

t^2 = [-b ± sqrt(b^2 - 4ac)] / (2a)

In this case, the equation can be rewritten as:

(t^2)^2 + 4(t^2) + 4 = 0

So, a = 1, b = 4, and c = 4.

Now, we can substitute these values into the formula:

t^2 = [-4 ± sqrt((4)^2 - 414)] / (2*1) t^2 = [-4 ± sqrt(16 - 16)] / 2 t^2 = [-4 ± sqrt(0)] / 2 t^2 = [-4 ± 0] / 2 t^2 = -2 or -2

Since t^2 cannot be negative, there are no real roots for the given equation.