Let `f(x) = ax^2 + bx +C,a,b,c in R`.It is given `|f(x)|<=1,|x|<=1` The possible value of `|a + c|` ,if `8/3a^2+2b^2` is maximum, is given by

Let f(x) = ax^(2) + bx + c, a, b, c, in R and equation f(x) - x = 0 has imaginary roots alpha, beta . If r, s be the roots of f(f(x)) - x = 0 , then |(2,alpha,delta),(beta,0,alpha),(gamma,beta,1)| is

Let f(x) = ax^(2) + bx + c, a, b, c, in R and equation f(x) - x = 0 has imaginary roots alpha, beta . If r, s be the roots of f(f(x)) - x = 0 , then |(2,alpha,delta),(beta,0,alpha),(gamma,beta,1)| is

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

Let f(x) = ax^(3) + bx +c . Then when f is odd,

Let f(x)=ax^(2)+bx+c AA a,b,c in R,a!=0 satisfying f(1)+f(2)=0. Then,the quadratic equation f(x)=0 must have :

Let f:[0,5] -> [0,5) be an invertible function defined by f(x) = ax^2 + bx + C, where a, b, c in R, abc != 0, then one of the root of the equation cx^2 + bx + a = 0 is:

Let f:[0,5] -> [0,5) be an invertible function defined by f(x) = ax^2 + bx + C, where a, b, c in R, abc != 0, then one of the root of the equation cx^2 + bx + a = 0 is:

Let R rarr f(x) = x^3 + ax^2 + bx + c sin x, a, b, c in R Find the condition that should be imposed on a, b, c so that the given function becomes invertible ?