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Question

If the difference between the roots of the equation x2+ax+8=0 is 2, write the values of a.

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Solution

Given: x2 + ax + 8 = 0.
Let α and β are the roots of the equation.
Sum of the roots = α + β =-a1 =-a.

Product of the roots = αβ = 81 = 8
Given: α - β = 2

Then, α+ β2 - α - β2 = 4αβ α + β2 - 22 = 4×8 α + β2 - 4 = 32 α + β2 = 32 + 4 = 36α + β = ± 6
α + β =-a = ±6
a = ±6

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