x2-4x+3=0
To solve the quadratic equation \(x^2 - 4x + 3 = 0\), you can use the factoring method.
Factoring: Look for two numbers that multiply to \(3\) (the constant term) and add to \(-4\) (the coefficient of \(x\)).
The numbers \(-1\) and \(-3\) work because: \(-1 \times -3 = 3\) and \(-1 + -3 = -4\).
Thus, you can factor the equation as: \[ (x - 1)(x - 3) = 0 \]
Setting each factor equal to zero: \[ x - 1 = 0 \quad \text{or} \quad x - 3 = 0 \] This gives you: \[ x = 1 \quad \text{or} \quad x = 3 \]
Solutions: The solutions to the equation \(x^2 - 4x + 3 = 0\) are: \[ x = 1 \quad \text{and} \quad x = 3 \]
You can verify these solutions by substituting them back into the original equation.
For \(x = 1\): \[ (1)^2 - 4(1) + 3 = 1 - 4 + 3 = 0 \] For \(x = 3\): \[ (3)^2 - 4(3) + 3 = 9 - 12 + 3 = 0 \]
Both solutions satisfy the equation, confirming that \(x = 1\) and \(x = 3\) are correct.
