Discussion

Explanation:

α and β be two distinct root of 2x² – 6x + k = 0,
∴ α + β = -(-6)/2 = 3
And, α × β = k/2 = k/2

Now, 3 and k are the roots of the equation x² + px + p = 0.
∴ Sum of the roots = 3 + k/2 = -(p)/1 = -p    …(1)
∴ Product of the roots = 3 × k/2 = (p)/1 = p    …(2)

(1) + (2)
⇒ 3 + k/2 + 3k/2 = p – p = 0
⇒ k = -3/2

⇒ p = -9/4    [from (2)]

Now, we need to find 8(k - p)
= $8\left(\frac{-3}{2}-\frac{-9}{4}\right)$
= $8\left(\frac{3}{4}\right)$
= 6

Hence, 6.

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