Question

17kx^2 + 22x + 5k has two equal roots. Find k.

Answer 1

The polynomial must be a perfect square. Does that help?

Answer 2

i.e. (ax+b)^2 = 17kx^2 + 22x + 5k

Answer 3

If it has two equal roots, then \[22^{2}-4\times17\times k \times 5 \times k = 0\]Wich gives \[k=\pm \frac{ 11 }{ \sqrt{85}}\]
That comes from Baskaras formula, wich you get by doing what @CliffSedge said.