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MATH / The polynomial 4x⁴−ax³+bx²−cx+5, where a, b, and c are real coefficients, has four positive real roots r₁, r₂, r₃, r₄, such that (r₁)/(2)+(r₂)/(4)+(r₃)/(5)+(r₄)/(8)=1.Find a.

Problem

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problem

The polynomial 4x4−ax3+bx2−cx+5,4x^4 - ax^3 + bx^2 - cx + 5, where a,a, b,b, and cc are real coefficients, has four positive real roots r1,r_1, r2,r_2, r3,r_3, r4,r_4, such that r12+r24+r35+r48=1.\frac{r_1}{2} + \frac{r_2}{4} + \frac{r_3}{5} + \frac{r_4}{8} = 1.Find a.a.
Plain-text mathematical notation (without MathML)
The polynomial 4x⁴−ax³+bx²−cx+5, where a, b, and c are real coefficients, has four positive real roots r₁, r₂, r₃, r₄, such that
(r₁)/(2)+(r₂)/(4)+(r₃)/(5)+(r₄)/(8)=1.Find a.
Original LaTeX notation
The polynomial $4x^4 - ax^3 + bx^2 - cx + 5,$ where $a,$ $b,$ and $c$ are real coefficients, has four positive real roots $r_1,$ $r_2,$ $r_3,$ $r_4,$ such that
\[\frac{r_1}{2} + \frac{r_2}{4} + \frac{r_3}{5} + \frac{r_4}{8} = 1.\]Find $a.$

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
adeab690-1e45-5836-b353-bdcf7a2b6c6a
task_key
intermediate~5falgebra--test--adeab690-1e45-5836-b353-bdcf7a2b6c6a
task_revision_id
1
config / split
intermediate_algebra / test

Official source

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