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Question
If α and β are the zeroes of the polynomial x2 + x − 2, then find the value of `alpha/beta+beta/alpha`
Solution
Step 1: Use Sum and Product of Roots
Sum of roots: `alpha+beta = ("−coefficient of x")/("coefficient of" x^2)`
Product of roots: `alpha beta = ("constant term")/("coefficient of" x^2) = -2/1 = -2`
Step 2: Find `alpha/beta + beta/alpha`
`alpha/beta + beta/alpha = (alpha^2 + beta^2)/(alphabeta)`
α2 + β2 = (α + β)2 − 2αβ
Substituting known values:
α2 + β2 = (−1) 2 − 2(−2)
= 1 + 4 = 5
`alpha/beta + beta/alpha = 5/-2`
`= -5/2`
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