Enter the number of complex zeros for the polynomial function in the box. f(x) = x⁴ + 5x² + 6

Solution:

Given, f(x) = x⁴ + 5x² + 6

We have to enter the number of complex zeros for the polynomial function.

Let x² = a

Now, f(x) = a² + 5a + 6

On factorising,

a² + 5a + 6 = 0

a² + 3a + 2a + 6 = 0

a(a + 3) + 2(a + 3) = 0

(a + 2)(a + 3) = 0

Now, a + 2 = 0

a = -2

Also, a + 3 = 0

a = -3

We know, a = x²

So, x² = -2

Taking square root,

x = ±√2i

Also, x² = -3

Taking square root,

x = ±√3i

The complex zeros are +√2i, -√2i, +√3i and -√3i.

Therefore, the number of complex zeros is 4.

---

Enter the number of complex zeros for the polynomial function in the box. f(x) = x⁴ + 5x² + 6

Summary:

The number of complex zeros for the polynomial function in the box. f(x) = x⁴ + 5x² + 6 is 4.