Solve x^2-5x+6 = 0
Solve ax² + bx + c = 0 using the quadratic formula with discriminant analysis.
x2-5x+6=0
Solve by factoring the quadratic and applying the zero product property:
We need two numbers that multiply to 6 (the constant term) and add to -5 (the coefficient of x):
-3 × -2 = 6 and -3 + (-2) = -5
Write the factored form using these numbers:
(x - 3)(x - 2) = 0
If a product equals zero, at least one of the factors must be zero. Set each factor equal to zero and solve:
x − 3 = 0 → x = 3
x − 2 = 0 → x = 2
x = 2, 3
How to solve x^2-5x+6 = 0
To solve x^2-5x+6 = 0, we can try factoring, use the quadratic formula, or complete the square. The solution is x = 2, 3.
This is a second-degree quadratic equation — the highest power of the variable is 2. Quadratic equations can have two real roots, one repeated root, or two complex roots.
Frequently asked questions
What is the answer to x^2-5x+6 = 0?
The answer is x = 2, 3.
What method is used?
factoring when possible, or the quadratic formula x = (−b ± √(b²−4ac)) / 2a. The discriminant b²−4ac determines the number and type of solutions.
How do I verify this?
Substituting the solution(s) back into x^2-5x+6 = 0 confirms both sides are equal.