Let `f(x) = ax^2 + bx + c`, where a, b, care integers. Suppose `f(1) = 0, 40 < f(6) < 50, 60 < f(7) < 70, and 1000t < f(50)< 1000 (t + 1)` for some integer t. Then the value of t is

Let f (x) = ax^(2)+bx+c where a, b, c are integers. Suppose f (1)=0, 40 lt f (6) lt 50, 60 lt f (7) lt 70, and 1000t lt f(50) lt 1000(t+1) for some integer t. Then the value fo t is

Let f(x) = a x^2 + bx + c , where a, b, c in R, a!=0 . Suppose |f(x)| leq1, x in [0,1] , then

Let f(x) = a x^2 + bx + c , where a, b, c in R, a!=0 . Suppose |f(x)| leq1, x in [0,1] , then

Let f(x) = a x^2 + bx + c , where a, b, c in R, a!=0 . Suppose |f(x)| leq1, x in [0,1] , then

Let f(x) = a x^2 + bx + c , where a, b, c in R, a!=0 . Suppose |f(x)| leq1, x in [0,1] , then

Let f(x) = x^3 + ax^2 + bx + c and g(x) = x^3 + bx^2 + cx + a , where a, b, c are integers. Suppose that the following conditions hold- (a) f(1) = 0 , (b) the roots of g(x) = 0 are the squares of the roots of f(x) = 0. Find the value of: a^(2013) + b^(2013) + c^(2013)

Let f(x) =ax^2+bx+c where a,b,c are real numbers. Suppose f(x)!=x for any real number x. Then the number of solutions for f(f(x))=x in real numbers x is

Let f (x) =ax ^(2) +bx+c, where a,b,c are integers and a gt 1. If f (x) takes the value p, a prime for two distinct integer values of x, then the number of integer values of x for which f (x) takes the value 2p is :