Which of the following equations has no real roots?

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Question: Which of the following equations has no real roots?

Options:

Correct Answer: x^2 + 4x + 5 = 0

Solution:

The discriminant for x^2 + 4x + 5 is negative (16 - 20 < 0), indicating no real roots.

Which of the following equations has no real roots?

Which of the following equations has no real roots?

Step 1: Identify the equation you are analyzing. In this case, it is x^2 + 4x + 5.
Step 2: Recognize that to find the roots of a quadratic equation, we can use the discriminant formula, which is b^2 - 4ac.
Step 3: Identify the coefficients a, b, and c from the equation. Here, a = 1, b = 4, and c = 5.
Step 4: Calculate the discriminant using the formula: b^2 - 4ac. Substitute the values: 4^2 - 4(1)(5).
Step 5: Perform the calculations: 4^2 = 16 and 4(1)(5) = 20. So, the discriminant is 16 - 20.
Step 6: Simplify the result: 16 - 20 = -4.
Step 7: Determine the nature of the roots based on the discriminant. If the discriminant is negative (like -4), it means there are no real roots.

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