GraphingCalc

Quadratic Equation

Solve x^2 - 5x + 6 = 0

Answer

x = 3 or x = 2

Working

  1. Identify the form

    Bring everything to one side to get a quadratic of the form ax² + bx + c = 0, with a = 1, b = -5 and c = 6.

  2. Compute the discriminant

    The discriminant is b² − 4ac = (-5)² − 4(1)(6) = 1.

  3. Apply the quadratic formula

    The discriminant is positive, so there are two distinct real roots. Substituting into x = (−b ± √(b² − 4ac)) / 2a gives x = (5 ± 1) / 2.

  4. Read off the solutions

    So x = 3 or x = 2.

Equations

Intermediate equations in the working
ExpressionResult
b² − 4ac = (-5)² − 4(1)(6)1
Plot these rootsHow to graph a parabola

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