Question

If the roots of the equation (m − n)z2 + (n − k)z + (k − m) = 0 are coincident, then the relation between k, m, and n is?(plss give complete solution?)

Answer 1

The roots are coincident or it has equal roots.

b² - 4ac = 0
⇒ (n-k)² - 4(m-n)(k-m) = 0
⇒ n² + k² - 2nk - 4(mk - m² - nk + nm) = 0
⇒ n² + k² - 2nk - 4mk + 4m² + 4nk - 4nm = 0
⇒ 4m² + n² + k² + 2nk - 4mk - 4nm = 0
⇒ (2m)² + n² + k² + 2×n×k - 2×2m×k - 2×2m×n = 0
⇒ (-2m)² + n² + k² + 2×n×k + 2×(-2m)×k + 2×(-2m)×n = 0
⇒ (-2m+n+k)² = 0
⇒ -2m + n + k = 0
⇒ n+k=2m

Answer 2

Answer:

N+K=2M my answer

Step-by-step explanation:

this is right