Find the value of the discriminant. Then describe the number and type of roots for the equation. x2 + x + 7 = 0

The value of the discriminate is - 27 and there are 2 complex roots

Step-by-step explanation:

* Lets explain what is discriminant

- The form of the quadratic equation is y = ax² + bx + c

- The roots of the equation is the values of x when y = 0

- There are three types of roots:

# Two different real roots

# One real root

# No real roots or two complex roots

- We can know the types of roots of the equation without solve it by

using the discriminant which depends on the value of a, b, c

- The discriminant = b² - 4ac, where a is the coefficient of x², b is the

coefficient of x and c is the numerical term

# If b² - 4ac > 0, then there are two different real roots

# If b² - 4ac = 0, then there is one real root

# If b² - 4ac < 0, then there is no real root (2 complex roots)

* Lets solve the problem

∵ x² + x + 7 = 0

∴ a = 1, b = 1, c = 7

∵ The discriminant = b² - 4ac

∴ The discriminant = (1) - 4 (1) (7) = 1 - 28 = - 27

∵ - 27 < 0

∴ There is no real solution there are two complex roots

* The value of the discriminate is - 27 and there are 2 complex roots