If the roots of the equation x^2 + 5x + 6 = 0 are a and b, what is the value of

If the roots of the equation x^2 + 5x + 6 = 0 are a and b, what is the value of a + b?

If the roots of the equation x^2 + 5x + 6 = 0 are a and b, what is the value of a + b?

Correct Answer: -5

Step 1: Identify the equation given, which is x^2 + 5x + 6 = 0.
Step 2: Recognize that this is a quadratic equation in the form of ax^2 + bx + c = 0.
Step 3: Identify the coefficients: a = 1, b = 5, and c = 6.
Step 4: Use Vieta's formulas, which state that for a quadratic equation, the sum of the roots (a + b) is equal to -b/a.
Step 5: Substitute the values of b and a into the formula: -b/a = -5/1.
Step 6: Calculate -5/1, which equals -5.
Step 7: Conclude that the value of a + b is -5.

Quadratic Equations – Understanding the properties of quadratic equations, specifically how to find the sum and product of roots using Vieta's formulas.
Vieta's Formulas – A mathematical theorem that relates the coefficients of a polynomial to sums and products of its roots.