For the equation x^2 + 2x + k = 0 to have one root equal to 1, what is the value

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Question: For the equation x^2 + 2x + k = 0 to have one root equal to 1, what is the value of k?

Options:

Correct Answer: 1

Solution:

Substituting x = 1 into the equation gives 1^2 + 2*1 + k = 0 => 1 + 2 + k = 0 => k = -3.

For the equation x^2 + 2x + k = 0 to have one root equal to 1, what is the value of k?

For the equation x^2 + 2x + k = 0 to have one root equal to 1, what is the value of k?

Step 1: Start with the equation x^2 + 2x + k = 0.
Step 2: We know that one root of the equation is 1, so we will substitute x = 1 into the equation.
Step 3: Substitute x = 1 into the equation: 1^2 + 2*1 + k = 0.
Step 4: Calculate 1^2, which is 1.
Step 5: Calculate 2*1, which is 2.
Step 6: Now, the equation looks like this: 1 + 2 + k = 0.
Step 7: Combine 1 and 2 to get 3, so the equation is now 3 + k = 0.
Step 8: To find k, we need to isolate it. Subtract 3 from both sides: k = -3.

Quadratic Equations – Understanding the conditions for a quadratic equation to have specific roots.
Substitution – Using substitution to find unknown parameters in an equation.