find the family of quadratic functions (in simplest form) with roots at 2 plus/minus 3 root 5

The "a" is just there like a constant to create variations of the graph.

So we have......

[x - (3√5 + 2)] * [x + (3√5 - 2)] = 0

x^2 - (3√5 + 2)x + (3√5 - 2)x - [ 45 - 4] = 0

x^2 - 4x - 41 = 0

I'm not exactly sure what you mean by "family,' but any multiples of this function would produce the same roots.

Anyone else have other approaches/ideas ???

Am I missing something???

Thanks, Aziz.....I needed to put the "a" in there to indicate "multiples" or "family"