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

If the quadratic equation x^2 + mx + n = 0 has roots 2 and -3, what is the value of m + n?

If the quadratic equation x^2 + mx + n = 0 has roots 2 and -3, what is the value of m + n?

Step 1: Identify the roots of the quadratic equation, which are given as 2 and -3.
Step 2: Use Vieta's formulas, which tell us that for a quadratic equation of the form x^2 + mx + n = 0, the sum of the roots (2 + (-3)) is equal to -m.
Step 3: Calculate the sum of the roots: 2 + (-3) = -1.
Step 4: Set the sum of the roots equal to -m: -1 = -m.
Step 5: Solve for m: m = 1.
Step 6: Use Vieta's formulas again, which state that the product of the roots (2 * -3) is equal to n.
Step 7: Calculate the product of the roots: 2 * -3 = -6.
Step 8: Set the product of the roots equal to n: n = -6.
Step 9: Now, find m + n: m + n = 1 + (-6).
Step 10: Calculate m + n: 1 - 6 = -5.

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 derive coefficients from given roots.