What is the sum of the roots of the equation f(x) = x^2 - 5x + 6?

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Question: What is the sum of the roots of the equation f(x) = x^2 - 5x + 6?

Options:

Correct Answer: 5

Solution:

The sum of the roots of ax^2 + bx + c = 0 is -b/a. Here, sum = 5.

What is the sum of the roots of the equation f(x) = x^2 - 5x + 6?

What is the sum of the roots of the equation f(x) = x^2 - 5x + 6?

Step 1: Identify the equation given, which is f(x) = x^2 - 5x + 6.
Step 2: Recognize that this is a quadratic equation in the form ax^2 + bx + c.
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: -(-5)/1.
Step 6: Simplify the expression: 5/1 = 5.
Step 7: Conclude that the sum of the roots is 5.

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