Question

alpha and beta are the zeroes of a quadratic polynomial ax2+bx+c then evaluate 1/alpha-1/beta

Answer 1

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

hope this helps

Answer 2

the following attachment is the solution of question