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

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Dear Student

In the aforementioned polynomial, let a^2= x.

Now, the polynomial becomes,

x^2+ 4x+ 5

Comparing with ax^2+ bx + c,

Here, b^2– 4ac = 4^2– 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.

Thanks