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If α, β, γ Are Are the Zeros of the Polynomial F(X) = X3 − Px2 + Qx − R, the 1 α β + 1 β γ + 1 γ α = - Mathematics

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Question

If α, β, γ are are the zeros of the polynomial f(x) = x3 − px2 + qx − r, the\[\frac{1}{\alpha\beta} + \frac{1}{\beta\gamma} + \frac{1}{\gamma\alpha} =\]

Answer in Brief
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Solution

We have to find the value of `1/(alphabeta)+1/(betay)+1/(yalpha)`

Given `alpha,beta,y` be the zeros of the polynomial f(x) = x3 − px2 + qx − r

`alpha + ß + y =  (-text{coefficient of }x^2)/(text{coefficient of } x^3)`

`= (-p)/1`

`= p`

`alphabetay= (-\text{Constant term})/(\text{Coefficient of}x^3)`

`(-(r))/1`

`= r`

Now we calculate the expression

`1/(alphabeta)+1/(betay)+1/(yalpha)= y/(alphabetay)+alpha/(alphabetay)+beta/(alphabetay)`

`1/(alphabeta)+1/(betay)+1/(yalpha)= (alpha+y+beta)/(alphabetay)`

`1/(alphabeta)+1/(betay)+1/(yalpha)= p/r`

Hence, the correct choice is `(b).`

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Chapter 2: Polynomials - Exercise 2.5 [Page 63]

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RD Sharma Mathematics [English] Class 10
Chapter 2 Polynomials
Exercise 2.5 | Q 19 | Page 63

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