Question

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

Answer 1

The number of roots are 2 and type of roots is complex

Explanation:

Points to remember

Discriminant of a quadratic equation ax² + bx + c = 0

x = b² - 4ac

To find the discriminant of the given equation

Here quadratic equation be x² + x + 7 = 0

a = 1, b = 1 and c = 7

discriminant = b² - 4ac

= 1² - (4 * 1 * 7)

= 1 - 28

= -27

To find number and type of roots

Here discriminant is negative

Therefore the number of roots are 2 and type of roots is complex

Answer 2

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

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