What are the roots of the quadratic equation x^2 - 5x + 6 = 0?
Practice Questions
1 question
Q1
What are the roots of the quadratic equation x^2 - 5x + 6 = 0?
x = 1, 6
x = 2, 3
x = -2, -3
x = 0, 6
Step 1: Factor the equation: (x - 2)(x - 3) = 0. Step 2: Set each factor to zero: x - 2 = 0 or x - 3 = 0. Step 3: Solutions are x = 2 and x = 3.
Questions & Step-by-step Solutions
1 item
Q
Q: What are the roots of the quadratic equation x^2 - 5x + 6 = 0?
Solution: Step 1: Factor the equation: (x - 2)(x - 3) = 0. Step 2: Set each factor to zero: x - 2 = 0 or x - 3 = 0. Step 3: Solutions are x = 2 and x = 3.
Steps: 4
Step 1: Factor the equation x^2 - 5x + 6 into two binomials. We look for two numbers that multiply to 6 (the constant term) and add to -5 (the coefficient of x). The numbers are -2 and -3. So, we can write the equation as (x - 2)(x - 3) = 0.
Step 2: Set each factor equal to zero. This gives us two equations: x - 2 = 0 and x - 3 = 0.
Step 3: Solve each equation. For x - 2 = 0, we add 2 to both sides to get x = 2. For x - 3 = 0, we add 3 to both sides to get x = 3.
Step 4: The solutions (or roots) of the quadratic equation are x = 2 and x = 3.
