12. The positive value of k for which the equality x3 + kx +64-0 and x

1.	12. The positive value of k for which the equality x3 + kx +64-0 and x2-8x +k0 which have real=0 and x2-8x + k = 0 which have realroots is
Answer» Solution:- Let D₁ and D₂ be the discriminant of the given equations and these will have equal roots only if D₁, D₂≥ 0 Or, if D₁ = (k² -4 × 64) ≥ 0 and D₂ = (64 - 4k) ≥ 0 Or, if k²≥ 256 and 4k ≤ 64Or, if k≥ 16 and k≤ 16Or, k = 16 Hence the positive value of k is 16

12. The positive value of k for which the equality x3 + kx +64-0 and x2-8x +k0 which have real=0 and x2-8x + k = 0 which have realroots is

Answer»

Solution:-

Let D₁ and D₂ be the discriminant of the given equations and these will have equal roots only if D₁, D₂≥ 0

Or, if D₁ = (k² -4 × 64) ≥ 0 and D₂ = (64 - 4k) ≥ 0

Or, if k²≥ 256 and 4k ≤ 64Or, if k≥ 16 and k≤ 16Or, k = 16

Hence the positive value of k is 16