If \alpha, \beta are roots of the equation 5(x-2020)(x-2022)+7(x-2021)(x-2023)=0, then

Sydney Stanley

Sydney Stanley

Answered question

2022-04-20

If α,β are roots of the equation 5(x2020)(x2022)+7(x2021)(x2023)=0, then find [α]+[β].

Answer & Explanation

Annie Levine

Annie Levine

Beginner2022-04-21Added 15 answers

Let f(x)=5(x2020)(x2022) with roots α<β. +7(x2021)(x2023)=0
f(2020) is positive and f(2021) is negative, so f(x)=0 for some value of 2020<x<2021. So [α]=2020
f(2022) is negative and f(2023) is positive, so f(x)=0 for some value of 2020<x<2023. So [β]=2020

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