Question

How many roots does y = x2 - 6x +9 have? It may help to graph the equation.

Answer 1

`\begin{gathered} x^2-6x+9=(x-a)(x-b) \\ x^2-6x+9=x^2+x(-a-b)+ab \\ \text{ } \\ \\ \text{thus a+b = 6 and ab=9} \end{gathered}`
`\begin{gathered} 9=3\cdot3\text{ and 3+3=6, thus } \\ a=3,\text{ b=3, } \\ \\ x^2-6x+9=(x-3)(x-3) \\ =(x-3)^2 \\ \\ \text{ there is only one root! and is x=3} \\ \\ \end{gathered}`