if alpha and beta are the zeroes of the polynomial x^2+8x+6 form polynomials whose zeroes are 1/aplha and 1/ beta
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αandβ are zeroes of x²+8x+6
to find polynomial whose zeroes are 1/α and 1/β
sum of zeroes α+β= -(8)/2= -4
product of zeroes αβ= 6/2= 3
sum of zeroes of new polynomial = 1/α +1/β = (α+β)/αβ= -4/3
product of zeroes of new polynomial =1/αβ = 1/3
let new polynomial be
k(ax²+bx+c) where k is a constant
1/α+1/β = -b/a = -4/3 ∴ b=-4 a=3
1/αβ= c/a= 1/3 ∴ c=1 a=3
∴the new polynomial will be
k(3x²-4x+1)
αandβ are zeroes of x²+8x+6
to find polynomial whose zeroes are 1/α and 1/β
sum of zeroes α+β= -(8)/2= -4
product of zeroes αβ= 6/2= 3
sum of zeroes of new polynomial = 1/α +1/β = (α+β)/αβ= -4/3
product of zeroes of new polynomial =1/αβ = 1/3
let new polynomial be
k(ax²+bx+c) where k is a constant
1/α+1/β = -b/a = -4/3 ∴ b=-4 a=3
1/αβ= c/a= 1/3 ∴ c=1 a=3
∴the new polynomial will be
k(3x²-4x+1)
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