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MATH / The parabola y=x² is tangent to the graph of y=x⁴+ax³+x²+bx+1 at two points. Find the positive difference between the x-coordinates of the points of tangency.

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problem

The parabola y=x2y = x^2 is tangent to the graph of y=x4+ax3+x2+bx+1y = x^4 + ax^3 + x^2 + bx + 1 at two points. Find the positive difference between the xx-coordinates of the points of tangency.
Plain-text mathematical notation (without MathML)
The parabola y=x² is tangent to the graph of y=x⁴+ax³+x²+bx+1 at two points.  Find the positive difference between the x-coordinates of the points of tangency.
Original LaTeX notation
The parabola $y = x^2$ is tangent to the graph of $y = x^4 + ax^3 + x^2 + bx + 1$ at two points.  Find the positive difference between the $x$-coordinates of the points of tangency.

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
e76ebc84-c349-56ab-bd33-5b5e579470d4
task_key
intermediate~5falgebra--test--e76ebc84-c349-56ab-bd33-5b5e579470d4
task_revision_id
1
config / split
intermediate_algebra / test

Official source

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