Let A=\ m: m. an integer and the roots of x^2+m x + 2020 = 0 are positive integers) and B=(n: n. an integer and the roots of x^2+2020 x+ n=0 are negative integers). Suppose a is the largest element of A and b is the

Correct answer: 26 α · β=2020 where α, β ∈ N and m=-(α+β) is least when α, β are 20 and 101. So a=-121 Now γ+ =-2020 where γ and are negative integers. So n=γ . is least if γ, σ are -1 and -2019. So b=2019 a+b=1898 Sum of digits =26

Olympiad workbook

Exam: Olympiad workbook
Subject: IOQM
Chapter: Quadratic Equation

Olympiad workbook · IOQM · Quadratic Equation

Let A=\ m: m. an integer and the roots of x^2+m x + 2020 = 0 are...

Let

A=\left\{m: m\right.

an integer and the roots of

x^2+m x

+ 2020 = 0 are positive integers)

and B=\left(n: n\right.

an integer and the roots of

x^2+2020 x+ n=0

are negative integers). Suppose

a

is the largest element of

A

and

b

is the smallest element of

B

. Find the sum of digits of

a+b

Correct answer

Step-by-step solution

\because \alpha \cdot \beta=2020

where

\alpha, \beta \in N

and

m=-(\alpha+\beta)

is least when

\alpha, \beta

are 20 and 101. So

a=-121

Now

\gamma+\delta=-2020

where

\gamma

and

\delta

are negative integers. So

n=\gamma . \delta

is least if

\gamma, \sigma

are -1 and -2019. So

b=2019

\Rightarrow a+b=1898

Sum of digits

=26

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