Mathematics 10 — Exercise Review · Q6

Full question

If x² + 2(1+k)x + k² = 0 has equal roots, find k.

Step-by-step solution

1. Set the discriminant to zero.

   $$-4\times k^2+{\left(2\times k+2\right)}^2=0$$

2. Expand: 4(1+2k+k²) − 4k² = 4+8k.

   $$8\times k+4=0$$

3. Subtract 4 then divide by 8.

   $$k=-\frac{1}{2}$$

Answer

The final answer is shown below.