Find the value of p for which the difference between the root of the equation x2 +px +8 =0 is 2
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Step-by-step explanation:
Given equation :
x² + px + 8 = 0 .....(i)
Let, α and β are roots of (i).
Then,
α + β = - p .....(ii)
and
αβ = 8 .....(iii)
Given :
α - β = 2
=> (α - β)² = 2²
=> (α + β)² - 4αβ = 4
=> p² - (4 × 8) = 4
=> p² - 32 = 4
=> p² = 32 + 4 = 36 = 6²
=> p = ± 6
So, the required values of p are
p = ± 6.
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