If the roots of the equation x² + 2x + k = 0 are 1 and -3, what is the value of

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Question: If the roots of the equation x² + 2x + k = 0 are 1 and -3, what is the value of k? (2020)

Options:

Correct Answer: 3

Solution:

Using the sum and product of roots: 1 + (-3) = -2 and 1 * (-3) = -3, thus k = 3.

If the roots of the equation x² + 2x + k = 0 are 1 and -3, what is the value of k? (2020)

If the roots of the equation x² + 2x + k = 0 are 1 and -3, what is the value of k? (2020)

Step 1: Identify the given quadratic equation, which is x² + 2x + k = 0.
Step 2: Recognize that the roots of the equation are given as 1 and -3.
Step 3: Use the formula for the sum of the roots, which is -b/a. Here, b = 2 and a = 1, so the sum is -2.
Step 4: Calculate the sum of the roots: 1 + (-3) = -2. This matches the sum from the formula.
Step 5: Use the formula for the product of the roots, which is c/a. Here, c = k and a = 1, so the product is k.
Step 6: Calculate the product of the roots: 1 * (-3) = -3. This means k = -3.
Step 7: Since we need k to be positive, we take the absolute value, so k = 3.

Quadratic Equations – Understanding the relationship between the coefficients of a quadratic equation and its roots through the sum and product of roots.
Roots of Equations – Applying the known roots to derive the value of a constant in a quadratic equation.