Answer:
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
Answer:
The number of roots are 2 and type of roots is complex
Step-by-step 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
