If the roots of the equation x² + 5x + 6 = 0 are a and b, what is the value of a

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Question: If the roots of the equation x² + 5x + 6 = 0 are a and b, what is the value of a + b? (2019)

Options:

Correct Answer: 5

Exam Year: 2019

Solution:

The sum of the roots is given by -b/a = -5/1 = -5.

If the roots of the equation x² + 5x + 6 = 0 are a and b, what is the value of a + b? (2019)

If the roots of the equation x² + 5x + 6 = 0 are a and b, what is the value of a + b? (2019)

Step 1: Identify the equation given, which is x² + 5x + 6 = 0.
Step 2: Recognize that this is a quadratic equation in the form of ax² + bx + c = 0.
Step 3: Identify the coefficients: a = 1, b = 5, and c = 6.
Step 4: Use the formula for the sum of the roots of a quadratic equation, which is -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 (the sum of the roots) is -5.

Quadratic Equations – Understanding the properties of quadratic equations, specifically the relationship between coefficients and roots.
Sum of Roots – Using Vieta's formulas to find the sum of the roots of a quadratic equation.