Math CentralQuandaries & Queries


Question from Lindah, a student:

how do I find quadratic with two given roots and a constant term?

Hi Lindah,

The quadratic $(x - r_1)(x - r_2)$ has roots $r_1$ and $r_2$ but so does $2 (x - r_1)(x - r_2)$ and $5 (x - r_1)(x - r_2).$ In fact for any constant $k,$ $k (x - r_1)(x - r_2)$ has roots $r_1$ and $r_2.$ If you know what the constant term is can you find the appropriate value of $k?$


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