Query about question "$f(x)=3 x^{2}+6 x+3$..." [1329]

https://www.gregmat.com/problems/quant?problem=fx3-x26-x3


In this problem, I multiplied the co-efficient of 3 with the constant 3 to get 9 and then factored the quadratic that way. By solving that way I got the lowest digit of x as -3. Is it wrong?

yes, because the lowest value of x is -1. This values gives the lowest value of y, 0 (which the q asked for).

Notice you got -3 because you multiplied by 3.

Why did you multiply by 3 though?