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

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

Options:

Correct Answer: -7

Solution:

The sum of the roots is -(-2 - 3) = 5, so m = 5. The product of the roots is (-2)(-3) = 6, so n = 6. Thus, m + n = 5 + 6 = 11.

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

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

Correct Answer: 11

Step 1: Identify the roots of the equation, which are given as -2 and -3.
Step 2: Use the formula for the sum of the roots, which is -m. Calculate the sum: -2 + (-3) = -5.
Step 3: Since the sum of the roots is -5, we have -m = -5. Therefore, m = 5.
Step 4: Use the formula for the product of the roots, which is n. Calculate the product: (-2) * (-3) = 6.
Step 5: Now we have m = 5 and n = 6.
Step 6: Add m and n together: m + n = 5 + 6.
Step 7: Calculate the final result: 5 + 6 = 11.

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