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Discriminant and the nature of roots sheet
3-mark answer frame

Find the values of k for which the equation 2x² + kx + 8 = 0 has two equal roots. Also find the roots.

How to lay out the answer. Follow the frame, then write it in your own words.

  1. 1 · Write what is given and what is to be found. 2x² + kx + 8 = 0 has equal roots. To find: k and the roots.
  2. 2 · Write the condition. For equal roots, D = b² − 4ac = 0.
  3. 3 · Identify a, b and c. a = 2, b = k, c = 8
  4. 4 · Solve for k. k² − 4(2)(8) = 0, so k² = 64 and k = ±8.
  5. 5 · Find the roots. Each root = −b/(2a) = −k/4. For k = 8: x = −2, −2. For k = −8: x = 2, 2.
  6. 6 · Check and box the answer. 2x² + 8x + 8 = 2(x + 2)² and 2x² − 8x + 8 = 2(x − 2)². Therefore k = ±8, with roots −2 (for k = 8) and 2 (for k = −8).

Scoring tip: Give both signs of k, and the roots for each. Writing only k = 8 loses a mark.