The quadratic equation x² + 10x + 72 = 0, the nature of the roots are imaginary.
The quadratic equation x² + 10x + 72 = 0 can be classified by examining the discriminant, which is the expression under the square root in the quadratic formula. The discriminant is given by b² - 4ac, where a, b, and c are the coefficients of the quadratic equation.
In this case, the coefficients are a = 1, b = 10, and c = 72. Calculating the discriminant, we get:
b² - 4ac = 10² - 4(1)(72) = 100 - 288 = -188
Since the discriminant is negative (-188), the quadratic equation has no real roots. Instead, it has complex roots, also known as imaginary roots. Complex roots consist of a real part and an imaginary part, which is denoted by the symbol "i".
Therefore, the correct answer is "Imaginary".