If one root of the equation x^2 + 3x + k = 0 is 1, what is the value of k?

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Question: If one root of the equation x^2 + 3x + k = 0 is 1, what is the value of k?

Options:

Correct Answer: -2

Solution:

Substituting x=1 into the equation gives 1^2 + 3*1 + k = 0, hence k = -4.

If one root of the equation x^2 + 3x + k = 0 is 1, what is the value of k?

If one root of the equation x^2 + 3x + k = 0 is 1, what is the value of k?

Step 1: Start with the equation x^2 + 3x + k = 0.
Step 2: We know that one root of the equation is 1, so we will substitute x with 1.
Step 3: Substitute x = 1 into the equation: 1^2 + 3*1 + k = 0.
Step 4: Calculate 1^2, which is 1.
Step 5: Calculate 3*1, which is 3.
Step 6: Now the equation looks like: 1 + 3 + k = 0.
Step 7: Combine 1 and 3 to get 4, so the equation is now: 4 + k = 0.
Step 8: To find k, subtract 4 from both sides: k = 0 - 4.
Step 9: Therefore, k = -4.

Quadratic Equations – Understanding how to substitute values into a quadratic equation to find unknown coefficients.
Roots of Equations – Identifying and using the roots of a quadratic equation to solve for unknowns.