Method 1 : By putting value x=1 you can fnd only Option (A) satisfies.
Method 2 : Assume a general quadratic polynomial P(x)=ax^2 +bx + c
P(1)=a+b+c=1
P(3)=9a+3b+c=27
P(4)=16a+4b+c=64
By solving these three system of equations you will get values of a,b,c as 8, -19, 12 respectively.
And by putting value of a,b,c the polynomial obtained will be 8x^2-9x+12=0
But this method is time taking. Go for this method if you are unable to eliminate options.