Question

If alpha and beta are two zeroes of polynomial ax^2+bx+c then form the polynomial who zeroes are 1/alpha and 1/beta

Answer 1

Hey mate!

Here's your answer!!
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Given polynomial: ax² + bx + c.

We already know that,

α + β = -b/a
=> a(α + β) = -b
=> -a(α + β) = b

Now, substituting this value of b in the problem,

=> 1/(aα + b) + 1/(aβ + b)
=> 1/(aα - a(α + β)) + 1/(aβ - a(α + β))
=> 1/(-aβ) + 1/(-aα)
=> -1/a (1/β + 1/α)
=> -1/a (α + β)/αβ
=> -1/a (-b/a)(c/a)
=> b/ac
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$hope \: it \: helps \: you...$

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