The roots of the equation x^2 - 3x + 2 = 0 are:

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Question: The roots of the equation x^2 - 3x + 2 = 0 are:

Options:

Correct Answer: 1 and 2

Solution:

Factoring gives (x-1)(x-2) = 0, so the roots are 1 and 2.

The roots of the equation x^2 - 3x + 2 = 0 are:

The roots of the equation x^2 - 3x + 2 = 0 are:

Step 1: Start with the equation x^2 - 3x + 2 = 0.
Step 2: Look for two numbers that multiply to 2 (the constant term) and add up to -3 (the coefficient of x).
Step 3: The numbers -1 and -2 work because -1 * -2 = 2 and -1 + -2 = -3.
Step 4: Rewrite the equation using these numbers: (x - 1)(x - 2) = 0.
Step 5: Set each factor equal to zero: x - 1 = 0 and x - 2 = 0.
Step 6: Solve for x in each equation: x = 1 and x = 2.
Step 7: The roots of the equation are 1 and 2.

Quadratic Equations – Understanding how to solve quadratic equations using factoring.
Factoring – Recognizing how to factor a quadratic expression into linear factors.
Roots of Equations – Identifying the solutions (roots) of a quadratic equation.