Question

Does the polynomial a4 + 4a2 + 5 = 0 have real zeroes?

Answer 1

In the aforementioned equation, let a2 = x.

Now, the equation becomes,

x2 + 4x2 + 5 = 0

Here, b2 – 4ac will be = 42 – 4(1)(5) = 16 – 20 = -4

So, D = b2 – 4ac < 0

As the discriminant (D) is negative, the given polynomial does not have real roots or zeroes.