If the roots of the equation x² + 2x + k = 0 are real and distinct, what is the

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Question: If the roots of the equation x² + 2x + k = 0 are real and distinct, what is the condition for k? (2020)

Options:

Correct Answer: k > 4

Solution:

The discriminant must be greater than zero: 2² - 4*1*k > 0, which simplifies to k < 1.

If the roots of the equation x² + 2x + k = 0 are real and distinct, what is the condition for k? (2020)

If the roots of the equation x² + 2x + k = 0 are real and distinct, what is the condition for k? (2020)

Step 1: Identify the equation given, which is x² + 2x + k = 0.
Step 2: Recognize that to find the roots of a quadratic equation, we use the discriminant formula, which is b² - 4ac.
Step 3: In our equation, a = 1, b = 2, and c = k.
Step 4: Substitute the values into the discriminant formula: 2² - 4*1*k.
Step 5: Calculate 2², which equals 4, so we have 4 - 4k.
Step 6: For the roots to be real and distinct, the discriminant must be greater than zero: 4 - 4k > 0.
Step 7: Rearrange the inequality: 4 > 4k.
Step 8: Divide both sides by 4: 1 > k.
Step 9: This means k must be less than 1 for the roots to be real and distinct.

Discriminant – The discriminant of a quadratic equation determines the nature of its roots; it is calculated as b² - 4ac.
Real and Distinct Roots – For the roots of a quadratic equation to be real and distinct, the discriminant must be greater than zero.