Answer:
f(x) = [tex]3x^{3} - 6x^{2} - 15x + 30[/tex]
Step-by-step explanation:
If [tex]\sqrt{5}[/tex] is a root, then so is -[tex]\sqrt{5}[/tex]
f(x) = 3(x + [tex]\sqrt{5}[/tex])(x - [tex]\sqrt{5}[/tex])(x - 2)
= [tex]3(x^{2} - 5)(x - 2)[/tex]
= 3([tex]x^{3} - 2x^{2} - 5x + 10[/tex])
= [tex]3x^{3} - 6x^{2} - 15x + 30[/tex]
