solve the quadratic equation: $x^{2}-5x + 6 = 0$
solve the quadratic equation: $x^{2}-5x + 6 = 0$
Answer
Explanation:
Step1: Factor the quadratic equation
For the quadratic equation (x^{2}-5x + 6=0), we need to find two numbers that multiply to (6) (the constant term) and add up to (-5) (the coefficient of (x)). The numbers are (-2) and (-3). So, we can factor the equation as ((x - 2)(x - 3)=0).
Step2: Use the zero - product property
If (ab = 0), then either (a=0) or (b = 0). For ((x - 2)(x - 3)=0), we set each factor equal to zero:
- If (x-2=0), then (x = 2).
- If (x - 3=0), then (x=3).
Answer:
(x = 2) or (x = 3)