Question

If alpha and beta are the zeroes of x2-(k+6)x +2(2k-1)find k if alpha +beta =1/2 alpha into beta

Answer 1

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Answer 2

x² + (k + 6)x + 2(2k - 1)

⇒ α + β = k + 6

⇒ αβ = 2(2k - 1)

Given that α + β = 1/2 αβ, find x:

k + 6 = 1/2 [2(2k - 1)]

Distribute 1/2:

k + 6 = 2k - 1

Subtract k from both sides:

6 = k - 1

Add 1 to both sides:

7 = k

Switch sides:

k = 7

Answer: k = 7