Question

if alpha and beta are zeroes of the polynomial 6y square -7y+2 ; find a quadratic polynomial whose zeroes are 1/alpha, 1/beta.

Answer 1

α and β are the zeroes of the polynomial 6y²-7y+2
∴α+β=-b/a=7/6
  αβ=c/a=1/3

for the new polynomial,
sum of zeroes=1/α+1/β=α+β/αβ=7/6*3=7/2
product of zeroes=1/α*1/β=1/αβ=3

∴new polynomial=y²-(sum of zeroes)y+(product of zeroes)
                             =y²-7/2y+3
                             =2y²-7y+6

Answer 2

Here is your answer user.