If the quadratic equation x² + 5x + k = 0 has roots -2 and -3, find k. (2020)

If the quadratic equation x² + 5x + k = 0 has roots -2 and -3, find k. (2020)

Step 1: Understand that the roots of the quadratic equation are the values of x that make the equation equal to zero.
Step 2: Identify the given roots, which are -2 and -3.
Step 3: Use the property of quadratic equations that states the product of the roots (r1 and r2) is equal to k when the equation is in the form x² + bx + k = 0.
Step 4: Calculate the product of the roots: (-2) * (-3).
Step 5: Perform the multiplication: (-2) * (-3) = 6.
Step 6: Conclude that k = 6.

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