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MATH / Let a and b be real numbers such that the quadratic equations x²+ax+b=0 and ax²+bx+1=0 have a root in common. Enter all possible values of a+b, separated by commas.

Problem

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problem

Let aa and bb be real numbers such that the quadratic equations x2+ax+b=0x^2 + ax + b = 0 and ax2+bx+1=0ax^2 + bx + 1 = 0 have a root in common. Enter all possible values of a+b,a + b, separated by commas.
Plain-text mathematical notation (without MathML)
Let a and b be real numbers such that the quadratic equations x²+ax+b=0 and ax²+bx+1=0 have a root in common.  Enter all possible values of a+b, separated by commas.
Original LaTeX notation
Let $a$ and $b$ be real numbers such that the quadratic equations $x^2 + ax + b = 0$ and $ax^2 + bx + 1 = 0$ have a root in common.  Enter all possible values of $a + b,$ separated by commas.

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
90d0ad14-476f-5230-b4ad-f104f843500e
task_key
intermediate~5falgebra--test--90d0ad14-476f-5230-b4ad-f104f843500e
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import