quadratic equation

[man111]

find the quadratic equation of [tex]f(x)[/tex] such that [tex]f(x)\leq0[/tex] for all [tex]x \in [2,3][/tex] and coefficient of [tex]x^2[/tex] is one of the roots of [tex]x^2-x-2=0[/tex]

[rashi101]

[tex]F(x)= 2x^2-10x+12[/tex]
Am I right?

[man111]

Yes I have also got The same thing i.e [tex]f(x) = 2.(x-2)(x-3)[/tex]