Question

If α, β are zeroes of the quadratic polynomial x² – 5x + 6, form another quadratic polynomial whose zeroes are `1/α, 1/β`.

Answer 1

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