Answer:

1. discriminant: 0

nature of the roots: real, rational and equal

2. discriminant: 45

nature of the roots: real, irrational and unequal

Answer:

1. x² + 6x + 9 = 0

discriminant - 6² - 4 (1) (9)

nature of the roots - two real number of solution

2. x² + 9x + 20 = 0

discriminant - 9² - 4 (1) (20)

nature of the roots - two real number of solution

Step-by-step explanation:

1. x² + 6x + 9 = 0

1 6 9 -- value of a b c

6² - 4 (1) (9) -- discriminant b² -4ac

two real number of solution -- nature of the roots

2. x² + 9x + 20 = 0

1 9 20. -- value of a b c

9² - 4 (1) (20) -- discriminant b² - 4ac

two real number of solution -- nature of the roots