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Question
If a and are the zeros of the quadratic polynomial f(x) = ๐ฅ2 − ๐ฅ − 4, find the value of `1/alpha+1/beta-alphabeta`
Solution
Since ๐ผ + ๐ฝ are the zeroes of the polynomial: ๐ฅ2 − ๐ฅ − 4
Sum of the roots (α + β) = 1
Product of the roots (αβ) = −4
`1/alpha+1/beta-alphabeta`
`=(alpha+beta)/(alphabeta)-alphabeta`
`=(1/-4)+4=(-1/4)+4=(-1+16)/4=15/4`
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