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MATH / The quadratic x²+(3)/(2)x−1 has the following property: the roots, which are (1)/(2) and −2, are one less than the final two coefficients. Find a quadratic with leading term x² suc…

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problem

The quadratic x2+32x−1x^2 + \frac{3}{2} x - 1 has the following property: the roots, which are 12\frac{1}{2} and −2,-2, are one less than the final two coefficients. Find a quadratic with leading term x2x^2 such that the final two coefficients are both non-zero, and the roots are one more than these coefficients. Enter the roots of this quadratic.
Plain-text mathematical notation (without MathML)
The quadratic x²+(3)/(2)x−1 has the following property: the roots, which are (1)/(2) and −2, are one less than the final two coefficients.  Find a quadratic with leading term x² such that the final two coefficients are both non-zero, and the roots are one more than these coefficients.  Enter the roots of this quadratic.
Original LaTeX notation
The quadratic $x^2 + \frac{3}{2} x - 1$ has the following property: the roots, which are $\frac{1}{2}$ and $-2,$ are one less than the final two coefficients.  Find a quadratic with leading term $x^2$ such that the final two coefficients are both non-zero, and the roots are one more than these coefficients.  Enter the roots of this quadratic.

level

Level 4

type

Intermediate Algebra

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Source and history

task_id
52edbe3b-7007-54db-9365-38c3f79de467
task_key
intermediate~5falgebra--test--52edbe3b-7007-54db-9365-38c3f79de467
task_revision_id
1
config / split
intermediate_algebra / test

Official source

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