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Omni-MATH / For a real number r, the quadratics x²+(r−1)x+6 and x²+(2r+1)x+22 have a common real root. The sum of the possible values of r can be expressed as (a)/(b), where a,b are relatively…

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problem

For a real number rr, the quadratics x2+(r−1)x+6x^{2}+(r-1)x+6 and x2+(2r+1)x+22x^{2}+(2r+1)x+22 have a common real root. The sum of the possible values of rr can be expressed as ab\frac{a}{b}, where a,ba, b are relatively prime positive integers. Compute 100a+b100a+b.
Plain-text mathematical notation (without MathML)
For a real number r, the quadratics x²+(r−1)x+6 and x²+(2r+1)x+22 have a common real root. The sum of the possible values of r can be expressed as (a)/(b), where a,b are relatively prime positive integers. Compute 100a+b.
Original LaTeX notation
For a real number $r$, the quadratics $x^{2}+(r-1)x+6$ and $x^{2}+(2r+1)x+22$ have a common real root. The sum of the possible values of $r$ can be expressed as $\frac{a}{b}$, where $a, b$ are relatively prime positive integers. Compute $100a+b$.

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Source and history

task_id
3121c6e4-2759-5635-a60e-33d620380ca4
task_key
test--3121c6e4-2759-5635-a60e-33d620380ca4
task_revision_id
1
config / split
/ test

Official source

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