The roots of the equation x^2 + 3x + k = 0 are -1 and -2. What is the value of k

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Question: The roots of the equation x^2 + 3x + k = 0 are -1 and -2. What is the value of k? (2021)

Options:

Correct Answer: 2

Exam Year: 2021

Solution:

The sum of the roots is -1 + (-2) = -3, and the product is (-1)(-2) = 2. Thus, k = 2.

The roots of the equation x^2 + 3x + k = 0 are -1 and -2. What is the value of k? (2021)

The roots of the equation x^2 + 3x + k = 0 are -1 and -2. What is the value of k? (2021)

Step 1: Identify the given quadratic equation, which is x^2 + 3x + k = 0.
Step 2: Recognize that the roots of the equation are given as -1 and -2.
Step 3: Calculate the sum of the roots: -1 + (-2) = -3.
Step 4: According to the properties of quadratic equations, the sum of the roots is equal to -b/a. Here, b = 3 and a = 1, so -b/a = -3.
Step 5: Since the sum of the roots matches, we can proceed to find the product of the roots.
Step 6: Calculate the product of the roots: (-1) * (-2) = 2.
Step 7: According to the properties of quadratic equations, the product of the roots is equal to c/a. Here, c = k and a = 1, so c/a = k.
Step 8: Since the product of the roots is 2, we have k = 2.

Quadratic Equations – Understanding the relationship between the coefficients of a quadratic equation and its roots, specifically using Vieta's formulas.
Roots of Equations – Identifying and calculating the sum and product of the roots of a quadratic equation.