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Mathematics · Grades 10–12

The discriminant

For real coefficients with a ≠ 0: positive Δ gives two real roots; zero gives one repeated root; negative gives no real roots.

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The key idea

For real coefficients with a ≠ 0: positive Δ gives two real roots; zero gives one repeated root; negative gives no real roots.

Δ = b² − 4ac

Worked examples

Find the discriminant of 1x² + 15x + 5 = 0.

15² − 4 × 1 × 5 = 205

205

Find the discriminant of 8x² + 9x + 11 = 0.

9² − 4 × 8 × 11 = -271

-271

Try it yourself

  1. Find the discriminant of 4x² + 20x + 9 = 0.

  2. Find the discriminant of 3x² + 10x + 12 = 0.

Check your understanding

Answers and marking notes
  1. 256

    20² − 4 × 4 × 9 = 256

  2. -44

    10² − 4 × 3 × 12 = -44

Further reading and review references

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