Answer:

Answer:

ax² + bx +c =0

zeroes α,β

sum of roots = α+β = -b/a

products of roots = αβ = c/a

1/α - 1/β = β-α / αβ   ............(1)

β-a = √(b² - 4ac/a² )      putting this value

1/α - 1/β  = √(b²-4ac/a²)  / c/a   =  √b²-4ac / c

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Answer:

b^2/c^2

Step-by-step explanation:

1/alpha^2-1/beta^2

alpha^2+beta^2/(alpha.beta)^2

(-b/a)^2/(c/a)^2

b^2/a^2*c^2/a^2

=b^2/c^2