Question

find the positive value of k for which the equation x²+ kx + 64 =0 and x² - 8x + k =0 will both have real roots

Answer 1

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 ≤ 64

Or, if k ≥ 16 and k ≤ 16

Or, k = 16

Hence the positive value of k is 16

Answer.

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Answer 2

Answer:

Step-by-step explanation: