Question

plzz solve this question.............

Answer 1

Answer:

kx²+ 1-2(k-1)x + x² = 0

kx² + x² -2(k-1)x + 1 = 0

(k+1)x² -2(k-1)x + 1 = 0

we know that if b²-4ac = 0 of quadratic equation ax² + bx + c then roots are equal

so,

{-2(k-1)}² - 4×(k+1)×1=0

4(k-1)²-4×(k+1)×1 = 0

(k-1)² - k -1 = 0

k² -3k = 0

k(k-3)

so either

k= 0 or k= 3

as k is non zero so k = 3

∴ the polynomial = 4x² - 4x + 1 = 0

(2x)² - 2× 2x +1² =0

(2x-1)² = 0

∴ x = 1/2 and 1/2