If the quadratic equation x^2 + 2x + k = 0 has roots 1 and -3, what is the value

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

If the quadratic equation x^2 + 2x + k = 0 has roots 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: Use the property of the product of the roots of a quadratic equation, which states that for an equation in the form ax^2 + bx + c = 0, the product of the roots (r1 * r2) is equal to c/a.
Step 4: In our equation, a = 1 and c = k. Therefore, the product of the roots (1 * -3) should equal k.
Step 5: Calculate the product of the roots: 1 * -3 = -3.
Step 6: Set the product equal to k: k = -3.
Step 7: 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 Quadratic Equations – Identifying and applying the properties of roots, including their sum and product.