Question

$\\ if \: \alpha \: and \: \beta \: are \: the \: zeros \: of \: the \: \: quadratic \: polynomial \: f{x} = x^{2} + x - 2 \: find \: the \: value \: of \: \frac{1 }{ \alpha } - \frac{1}{ \beta }$
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Answer 1

Answer:

Correct option is

B

3−5

Simple enough, provided you know the relationship between the coefficients of the polynomial equation and its roots . Here the polynomial equation is a quadratic equation; t² - 5t + 3 = 0 . If α, β be the roots of this equation then , we have ; α + β = 5 and α.β = 3 . Therefore, α⁴.β³ + α³.β⁴ = (α.β)³(α + β) = 3³ . 5 = 135.