Question

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

Answer 1

Step-by-step explanation:

Solution:

In the aforementioned polynomial, let a2 = x.

Now, the polynomial becomes,

x2 + 4x + 5

Comparing with ax2 + bx + c,

Here, b2 – 4ac = 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.