### Example 1

How many real number or complex number roots does the following equation have?

*y* = 3*x*^{2} + 3*x* + 3

### Example 2

How many real number or complex number roots does the following equation have?

*y* = *x*^{2} + *x* + 1

### Example 3

How many real number or complex number roots does the following equation have?

*y* = -*x*^{2} – 5*x* + 4

### Example 4

How many real number or complex number roots does the following equation have?

*y* = -3*x*^{2} + 6*x* – 3

### Example 5

How many real number or complex number roots does the following equation have?

*y* = *x*^{2} –2*x* – 2