Question:

Given the equation, 3x² + 4x = 8, which of the following is the nature of its roots?

Solution:

To find the nature of roots we need to solve the discriminant of the given equation.

• 3x² + 4x = 8

Identify the values of a, b and c.

• a = 3
• b = 4
• c = -8

Apply the formula in finding the descriminant. (Remember: D = b² - 4ac)

• D = b² - 4ac
• D = (4)² - 4(3)(-8)
• D = 16 - 4(-24)
• D = 16 + 96
• D = 112

Write the discriminant and identify if the nature of roots is equal or enequal to zero, or if it is below zero.

Answer:

• The discriminant is 122. Thus, the nature of roots is unequal, distinct and irrational.