If the roots of the equation x^2 + 5x + k = 0 are -2 and -3, what is the value o
Practice Questions
Q1
If the roots of the equation x^2 + 5x + k = 0 are -2 and -3, what is the value of k?
6
5
7
8
Questions & Step-by-Step Solutions
If the roots of the equation x^2 + 5x + k = 0 are -2 and -3, what is the value of k?
Step 1: Identify the given quadratic equation, which is x^2 + 5x + k = 0.
Step 2: Recognize that the roots of the equation are given as -2 and -3.
Step 3: Use the formula for the product of the roots of a quadratic equation, which states that the product of the roots (r1 * r2) is equal to k.
Step 4: Calculate the product of the roots: (-2) * (-3) = 6.
Step 5: Conclude that k is equal to the product of the roots, so k = 6.
Quadratic Equations – Understanding the relationship between the coefficients and the roots of a quadratic equation, specifically using Vieta's formulas.
Roots of Equations – Identifying and applying the properties of the roots of a quadratic equation to find unknown coefficients.
