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MATH / Let (a₁,b₁), (a₂,b₂), …, (a_(n),b_(n)) be the ordered pairs (a,b) of real numbers such that the polynomial p(x)=(x²+ax+b)²+a(x²+ax+b)−bhas exactly one real root and no nonreal comp…

Problem

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problem

Let (a1,b1),(a_1,b_1), (a2,b2),(a_2,b_2), …,\dots, (an,bn)(a_n,b_n) be the ordered pairs (a,b)(a,b) of real numbers such that the polynomial p(x)=(x2+ax+b)2+a(x2+ax+b)−bp(x) = (x^2 + ax + b)^2 +a(x^2 + ax + b) - bhas exactly one real root and no nonreal complex roots. Find a1+b1+a2+b2+…+an+bn.a_1 + b_1 + a_2 + b_2 + \dots + a_n + b_n.
Plain-text mathematical notation (without MathML)
Let (a₁,b₁), (a₂,b₂), …, (a_(n),b_(n)) be the ordered pairs (a,b) of real numbers such that the polynomial
p(x)=(x²+ax+b)²+a(x²+ax+b)−bhas exactly one real root and no nonreal complex roots.  Find a₁+b₁+a₂+b₂+…+a_(n)+b_(n).
Original LaTeX notation
Let $(a_1,b_1),$ $(a_2,b_2),$ $\dots,$ $(a_n,b_n)$ be the ordered pairs $(a,b)$ of real numbers such that the polynomial
\[p(x) = (x^2 + ax + b)^2 +a(x^2 + ax + b) - b\]has exactly one real root and no nonreal complex roots.  Find $a_1 + b_1 + a_2 + b_2 + \dots + a_n + b_n.$

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
fc2a527b-ee42-5ebf-8a12-716ff07ebaeb
task_key
intermediate~5falgebra--test--fc2a527b-ee42-5ebf-8a12-716ff07ebaeb
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import