Identify the roots f (x) = 3x^2-27

Factour ouf 3

f (x) = 3 (x²-9)

recognize diference of 2 perfect squres

a²-b² = (a+b) (a-b)

x²-9=x²-3² = (x+3) (x-3)

so

f (x) = 3 (x+3) (x-3)

seto to zero to find roots

0=3 (x+3) (x-3)

0=x+3

-3=x

0=x-3

3=x

roots at x=-3 and 3

The answer is x=3, - 3