What is the nature of the roots of the equation x² + 2x + 5 = 0? (2023)

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Question: What is the nature of the roots of the equation x² + 2x + 5 = 0? (2023)

Options:

Correct Answer: Complex

Exam Year: 2023

Solution:

The discriminant D = 2² - 4*1*5 = 4 - 20 = -16, which indicates complex roots.

What is the nature of the roots of the equation x² + 2x + 5 = 0? (2023)

What is the nature of the roots of the equation x² + 2x + 5 = 0? (2023)

Step 1: Identify the coefficients of the quadratic equation x² + 2x + 5 = 0. Here, a = 1, b = 2, and c = 5.
Step 2: Use the formula for the discriminant, D = b² - 4ac.
Step 3: Substitute the values of a, b, and c into the formula: D = 2² - 4*1*5.
Step 4: Calculate 2², which is 4.
Step 5: Calculate 4*1*5, which is 20.
Step 6: Subtract the two results: D = 4 - 20.
Step 7: Calculate the result: D = -16.
Step 8: Interpret the value of the discriminant. Since D is negative (-16), this means the equation has complex roots.

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