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If a and Are the Zeros of the Quadratic Polynomial F(X) = 𝑥2 − 𝑥 − 4, Find the Value of `1/Alpha+1/Beta-alphabeta` - CBSE Class 10 - Mathematics

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Question

If a and are the zeros of the quadratic polynomial f(x) = 𝑥2 − 𝑥 − 4, find the value of `1/alpha+1/beta-alphabeta`

Solution

Since 𝛼 + 𝛽 are the zeroes of the polynomial: 𝑥2 − 𝑥 − 4

Sum of the roots (α + β) = 1

Product of the roots (αβ) = −4

`1/alpha+1/beta-alphabeta`

`=(alpha+beta)/(alphabeta)-alphabeta`

`=(1/-4)+4=(-1/4)+4=(-1+16)/4=15/4`

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APPEARS IN

 RD Sharma Solution for 10 Mathematics (2018 to Current)
Chapter 2: Polynomials
Ex. 2.10 | Q: 4 | Page no. 34
Solution If a and Are the Zeros of the Quadratic Polynomial F(X) = 𝑥2 − 𝑥 − 4, Find the Value of `1/Alpha+1/Beta-alphabeta` Concept: Relationship Between Zeroes and Coefficients of a Polynomial.
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