X2-3x+2=0

To solve the quadratic equation \( x^2 - 3x + 2 = 0 \), we can factor it: 1. Look for two numbers that multiply to \( 2 \) (the constant term) and add up to \( -3 \) (the coefficient of \( x \)). 2. The numbers \( -1 \) and \( -2 \) meet these criteria: - \( -1 \times -2 = 2 \) - \( -1 + (-2) = -3 \) Thus, we can factor the equation as follows: \[ (x - 1)(x - 2) = 0 \] Now, set each factor equal to zero: 1. \( x - 1 = 0 \) ⟹ \( x = 1 \) 2. \( x - 2 = 0 \) ⟹ \( x = 2 \) So the solutions to the equation \( x^2 - 3x + 2 = 0 \) are: \[ x = 1 \quad \text{and} \quad x = 2 \]