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MATH / The equations x³+5x²+px+q=0 and x³+7x²+px+r=0 have two roots in common. If the third root of each equation is represented by x₁ and x₂ respectively, compute the ordered pair …

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problem

The equations x3+5x2+px+q=0x^3 + 5x^2 + px + q = 0 and x3+7x2+px+r=0x^3 + 7x^2 + px + r = 0 have two roots in common. If the third root of each equation is represented by x1x_1 and x2x_2 respectively, compute the ordered pair (x1,x2).(x_1,x_2).
Plain-text mathematical notation (without MathML)
The equations x³+5x²+px+q=0 and x³+7x²+px+r=0 have two roots in common.  If the third root of each equation is represented by x₁ and x₂ respectively, compute the ordered pair (x₁,x₂).
Original LaTeX notation
The equations $x^3 + 5x^2 + px + q = 0$ and $x^3 + 7x^2 + px + r = 0$ have two roots in common.  If the third root of each equation is represented by $x_1$ and $x_2$ respectively, compute the ordered pair $(x_1,x_2).$

level

Level 4

type

Intermediate Algebra

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Source and history

task_id
9ffd72bf-9fa7-58fc-8cac-69e96d754a28
task_key
intermediate~5falgebra--test--9ffd72bf-9fa7-58fc-8cac-69e96d754a28
task_revision_id
1
config / split
intermediate_algebra / test

Official source

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