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Question
If α, β are zeroes of the quadratic polynomial x2 – 5x + 6, form another quadratic polynomial whose zeroes are `1/α, 1/β`.
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Solution
p(x) = x2 − 5x + 6
`alpha+beta = (-"coefficient of" x)/("coefficient of" x^2) = (-(-5))/1 = 5`
`alpha beta = ("constant term")/("coefficient of" x^2) = 6/1 = 6`
`1/alpha + 1/beta = (alpha+beta)/(alpha beta) = 5/6`
`1/alpha xx 1/beta = 1/(alpha beta) = 1/6`
x2 − (A + B)x + AB = 0
`x^2 - (5/6)x + 1/6 = 0`
6x2 − 5x + 1 = 0
6x2 − 5x + 1
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