Final answer:
The quadratic equation x² + 8x - 9 = 0 has two distinct real roots because the discriminant, calculated as b² - 4ac, is positive (100 in this case).
Step-by-step explanation:
The equation x² + 8x - 9 = 0 is a quadratic equation of the form ax² + bx + c = 0. To find out how many roots this equation has, we can use the quadratic formula, which is given by:
x = ∛ [(b² - 4ac) / 2a].
In this equation, a = 1, b = 8 and c = -9. Before even using the quadratic formula, we can determine the number of roots by looking at the discriminant, which is the expression under the square root in the quadratic formula (b² - 4ac).
If we calculate the discriminant for this equation, we get:
Discriminant = b² - 4ac = (8)² - 4(1)(-9) = 64 + 36 = 100.
Since the discriminant is positive, it indicates that there are two distinct real roots for this quadratic equation.