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

If the roots of the equation x^2 + 3x + k = 0 are -1 and -2, what is the value of k? (2023)

If the roots of the equation x^2 + 3x + k = 0 are -1 and -2, what is the value of k? (2023)

Step 1: Understand that the equation x^2 + 3x + k = 0 is a quadratic equation.
Step 2: Recognize that the roots of the equation are given as -1 and -2.
Step 3: Use Vieta's formulas, which tell us that for a quadratic equation ax^2 + bx + c = 0, the sum of the roots (r1 + r2) is equal to -b/a and the product of the roots (r1 * r2) is equal to c/a.
Step 4: Identify the coefficients in the equation: a = 1, b = 3, and c = k.
Step 5: Calculate the product of the roots: (-1) * (-2) = 2.
Step 6: According to Vieta's formulas, the product of the roots is equal to c/a, which means k = 2.
Step 7: Conclude that the value of k is 2.

Vieta's Formulas – These formulas relate the coefficients of a polynomial to sums and products of its roots.
Quadratic Equations – Understanding the standard form of a quadratic equation and how to find its roots.