Question

For what values of k, does the following quadratic equation has equal roots.

k²x² - 2(2k - 1)x + 4 = 0

Answer 1

Since roots are equal

∴ d=0 (1)

k²x² - 2(2k -1)x + 4 = 0

d = b² – 4ac

d = (–2(k–1))² – 4 (k²) (4)

d = (–2k+2)² – 4k – 4

d = (–4k+2)² – 16k²

(∵ (a – b)² = a² + b² – 2ab)

d = 16k² – 16k + 4 – 16k²

d = –16k + 4

From (1), d = 0

∴ Equation will be:

0 = –16k + 4

16k = 4

k = 4/16

k = 1/4

∴ Values of k are is 1/4.