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If ๐›ผ and ๐›ฝ Are the Zeros of the Quadratic Polynomial F(X) = X2 โˆ’ 5x + 4, Find the Value of `1/Alpha-1/Beta-2alphabeta` - Mathematics

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Question

If ๐›ผ and ๐›ฝ are the zeros of the quadratic polynomial f(x) = x2 − 5x + 4, find the value of `1/alpha+1/beta-2alphabeta`

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Solution

Since ๐›ผ ๐‘Ž๐‘›๐‘‘ ๐›ฝ are the roots of the quadratic polynomial

f(x) = ๐‘ฅ2 − 5๐‘ฅ + 4

Sum of roots = α + β = 5

Product of roots = αβ = 4

`1/alpha+1/beta-2alphabeta=(beta+alpha)/(alphabeta)-2alphabeta=5/4-2xx4=5/4-8=(-27)/4`

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Chapter 2: Polynomials - Exercise 2.1 [Page 34]

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RD Sharma Mathematics [English] Class 10
Chapter 2 Polynomials
Exercise 2.1 | Q 7 | Page 34

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