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

If the roots of the equation x^2 + 2x + k = 0 are -1 and -3, what is the value of k? (2022)

If the roots of the equation x^2 + 2x + k = 0 are -1 and -3, what is the value of k? (2022)

Step 1: Identify the given quadratic equation, which is x^2 + 2x + k = 0.
Step 2: Recognize that the roots of the equation are given as -1 and -3.
Step 3: Calculate the sum of the roots: -1 + -3 = -4.
Step 4: According to the properties of quadratic equations, the sum of the roots is equal to -b/a. Here, b = 2 and a = 1, so -b/a = -2/1 = -2.
Step 5: Since the calculated sum of the roots (-4) does not match -2, we need to find k using the product of the roots instead.
Step 6: Calculate the product of the roots: (-1) * (-3) = 3.
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/1 = k.
Step 8: Set the product of the roots equal to k: k = 3.
Step 9: Conclude that the value of k is 3.

Quadratic Equations – Understanding the relationship between the coefficients of a quadratic equation and its roots, specifically using Vieta's formulas.
Roots of Equations – Calculating the sum and product of the roots to find unknown coefficients in a quadratic equation.