



 
Hi Sadiya, Suppose you were given the quadratic equation \[x^2 + 3x  10 = 0\] and you were asked to find the roots. I expect you would factor the quadratic to get \[(x  2)(x + 5) = 0\] and then conclude that the roots are $2$ and $5.$ If you know the roots are $2$ and $5$ can you trace the steps backwards to obtain the quadratic equation \[x^2 + 3x  10 = 0?\] Is this the only quadratic equation with roots $2$ and $5?$ What about \[7(x^2 + 3x  10) = 0\] or \[8(x^2 + 3x  10) = 0\] or \[k(x^2 + 3x  10) = 0\] where $k$ is any constant? Penny  


Math Central is supported by the University of Regina and the Imperial Oil Foundation. 