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Calculators · Algebra

Quadratic equation

Solve ax² + bx + c = 0: the discriminant, the kind of roots, the roots themselves and a check.

x = 3 or x = 0.5

The working

  1. The equation: 2x² − 7x + 3 = 0, so a = 2, b = −7, c = 3.
  2. Discriminant D = b² − 4ac = (−7)² − 4 × 2 × 3 = 49 − 24 = 25.
  3. D is positive, so there are two different real roots, and because D is a perfect square they are rational.
  4. x = (−b ± √D) ÷ 2a = (7 ± 5) ÷ 4.
  5. x = 3, and x = 1/2 = 0.5.
  6. Check with the zeroes: sum = 3.5 = −b/a = 3.5; product = 1.5 = c/a = 1.5.