If `f(x)=x^2+bx+c` and `f(2+t)=f(2-t)` for all real number t, then which of the following is true?

If f(x)=2 for all real numbers x, then f(x+2)=

Let f (x) =ax ^(2) + bx+ c,a gt = and f (2-x) =f (2+x) AA x in R and f (x) =0 has 2 distinct real roots, then which of the following is true ?

Let f (x) =ax ^(2) + bx+ c,a gt = and f (2-x) =f (2+x) AA x in R and f (x) =0 has 2 distinct real roots, then which of the following is true ?

Let f(x)=(1-x)^(2) sin^(2) x+x^(2) for all x in RR , and let g(x)=int_(1)^(x) ((2(t-1))/(t+1)-log t)f(t) dt for all x in (1, oo) . Which of the following is true?

Let f(x) = (1-x)^(2) sin^(2)x+ x^(2) for all x in IR and let g(x) = int_(1)^(x)((2(t-1))/(t+1)-lnt) f(t) dt for all x in (1,oo) . Which of the following is true ?

Let f(x)=(1-x)^(2)sin^(2)x+x^(2) for all x in IR, and let g(x)=int_(1)^(x)((2(t-1))/(t-1)-ln t)f(t) dt for all x,in(1,oo). Which of the following is true?

Let f(x)=(1-x)^2sin^2x+x^2 for all xinR and let g(x)=int_1^x((2(t-1))/(t+1)-Int) f(t)dt for all xin(1,oo) Which of the following is true ?

Let f(x) = (1 - x)^2 sin^2 x + x^2 for all x ∈ R, and let g(x) = ∫((2(t - 1))/(t + 1) - ln t)f(t)dt for t ∈ [1, x] for all x ∈ (1, ∞).Which of the following is true ?

Consider the quadratic function f(x)=ax^(2)+bx+c where a,b,c in R and a!=0, such that f(x)=f(2-x) for all real number x. The sum of the roots of f(x) is