The roots of the equation x² + 4x + k = 0 are 2 and -6. What is the value of k?

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Question: The roots of the equation x² + 4x + k = 0 are 2 and -6. What is the value of k? (2021)

Options:

Correct Answer: -8

Exam Year: 2021

Solution:

Using the product of roots: k = 2 * (-6) = -12. The sum is 2 + (-6) = -4, which matches.

The roots of the equation x² + 4x + k = 0 are 2 and -6. What is the value of k? (2021)

The roots of the equation x² + 4x + k = 0 are 2 and -6. What is the value of k? (2021)

Step 1: Identify the given quadratic equation, which is x² + 4x + k = 0.
Step 2: Recognize that the roots of the equation are given as 2 and -6.
Step 3: Use the formula for the product of the roots, which states that the product of the roots (r1 * r2) is equal to k.
Step 4: Calculate the product of the roots: 2 * (-6) = -12.
Step 5: Therefore, we find that k = -12.
Step 6: To verify, check the sum of the roots: 2 + (-6) = -4, which matches the coefficient of x in the equation (4).

Quadratic Equations – Understanding the relationship between the coefficients and the roots of a quadratic equation.
Vieta's Formulas – Using Vieta's formulas to relate the sum and product of the roots to the coefficients of the polynomial.