# State how many imaginary and real zeros the function has. f(x) = x^{3} + 5x^{2} + x + 5

**Solution:**

Given: Function f(x) = x^{3} + 5x^{2} + x + 5

Let us factorize by grouping

f(x) = (x^{3} + x) + (5x^{2} + 5)

Taking out the common

f(x) = x(x^{2} + 1) + 5(x^{2} + 1)

f(x) = (x + 5)(x^{2} + 1)

Now let us equate it to zero to find the imaginary and real zeros

⇒ x + 5 = 0

x = -5

⇒ x^{2} + 1 = 0

x^{2} = -1

x = ±√(-1)

We know that i^{2} = -1

x = ± i

Therefore, the function has one real and two imaginary zeros.

## State how many imaginary and real zeros the function has. f(x) = x^{3} + 5x^{2} + x + 5

**Summary:**

The function f(x) = x^{3} + 5x^{2} + x + 5 has two imaginary and one real zeros.

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