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Quadratic equations

Factoring, the discriminant and the quadratic formula.

A quadratic ax² + bx + c = 0 has up to two solutions — the points where the parabola crosses the x-axis. First try to factor; if that fails, the discriminant Δ = b² − 4ac tells you how many real roots there are before the quadratic formula tells you what they are.

Worked example: x^2 - 5x + 6 = 0

Algebra · Quadratic-Equations

Solve x^2 - 5x + 6 = 0

x^{2} - 5 x + 6 = 0

Step by step

  1. x^{2} - 5 x + 6 = 0

    Start from the equation as given.

  2. a = 1,\quad b = -5,\quad c = 6

    Read off the coefficients of the standard form ax² + bx + c = 0.

  3. \left(x - 3\right) \left(x - 2\right) = 0

    Factor the quadratic into two linear factors.

  4. x - 3 = 0 \;\Rightarrow\; x = 3

    A product is zero only when one of its factors is zero (zero-product property).

  5. x - 2 = 0 \;\Rightarrow\; x = 2

    A product is zero only when one of its factors is zero (zero-product property).

Reveal the answer
x = 3 \quad\text{or}\quad x = 2

Try your own

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