For which value of k does the equation x^2 + kx + 4 = 0 have one root equal to 2

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Question: For which value of k does the equation x^2 + kx + 4 = 0 have one root equal to 2?

Options:

Correct Answer: -2

Solution:

Substituting x = 2 into the equation gives 2^2 + 2k + 4 = 0, leading to k = -4.

For which value of k does the equation x^2 + kx + 4 = 0 have one root equal to 2?

For which value of k does the equation x^2 + kx + 4 = 0 have one root equal to 2?

Step 1: Start with the equation x^2 + kx + 4 = 0.
Step 2: We know one root of the equation is 2, so we will substitute x = 2 into the equation.
Step 3: Substitute 2 into the equation: 2^2 + k(2) + 4 = 0.
Step 4: Calculate 2^2, which is 4. Now the equation looks like: 4 + 2k + 4 = 0.
Step 5: Combine like terms: 4 + 4 = 8, so the equation is now 8 + 2k = 0.
Step 6: To isolate 2k, subtract 8 from both sides: 2k = -8.
Step 7: Now, divide both sides by 2 to solve for k: k = -4.

Quadratic Equations – Understanding the properties of quadratic equations and how to find roots.
Substitution – Using substitution to find unknown coefficients in polynomial equations.
Discriminant – Recognizing that a quadratic equation has one root when the discriminant is zero.