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