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Question
If ๐ผ and ๐ฝ are the zeros of the quadratic polynomial f(x) = x2 − 5x + 4, find the value of `1/alpha+1/beta-2alphabeta`
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Solution
Since ๐ผ ๐๐๐ ๐ฝ are the roots of the quadratic polynomial
f(x) = ๐ฅ2 − 5๐ฅ + 4
Sum of roots = α + β = 5
Product of roots = αβ = 4
`1/alpha+1/beta-2alphabeta=(beta+alpha)/(alphabeta)-2alphabeta=5/4-2xx4=5/4-8=(-27)/4`
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