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Omni-MATH / Let a,b,c,d be real numbers such that b−d≥5 and all zeros x₁,x₂,x₃, and x₄ of the polynomial P(x)=x⁴+ax³+bx²+cx+d are real. Find the smallest value the product …

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problem

Let a,b,c,da,b,c,d be real numbers such that b−d≥5b-d \ge 5 and all zeros x1,x2,x3,x_1, x_2, x_3, and x4x_4 of the polynomial P(x)=x4+ax3+bx2+cx+dP(x)=x^4+ax^3+bx^2+cx+d are real. Find the smallest value the product (x12+1)(x22+1)(x32+1)(x42+1)(x_1^2+1)(x_2^2+1)(x_3^2+1)(x_4^2+1) can take.
Plain-text mathematical notation (without MathML)
Let a,b,c,d be real numbers such that b−d≥5 and all zeros x₁,x₂,x₃, and x₄ of the polynomial P(x)=x⁴+ax³+bx²+cx+d are real. Find the smallest value the product (x₁²+1)(x₂²+1)(x₃²+1)(x₄²+1) can take.
Original LaTeX notation
Let $a,b,c,d$ be real numbers such that $b-d \ge 5$ and all zeros $x_1, x_2, x_3,$ and $x_4$ of the polynomial $P(x)=x^4+ax^3+bx^2+cx+d$ are real. Find the smallest value the product $(x_1^2+1)(x_2^2+1)(x_3^2+1)(x_4^2+1)$ can take.

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Source and history

task_id
baca908d-da8b-5348-9b41-f30865283ad5
task_key
test--baca908d-da8b-5348-9b41-f30865283ad5
task_revision_id
1
config / split
/ test

Official source

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