Let `f(x)` is `ax^(2)+bx+c;(3a+b>0)` and `f(x)>=0 AA x in R,` then minimum value of `(4a+2b+c)/(3a+b)` is

Let f(x) = ax^(2) - bx + c^(2), b ne 0 and f(x) ne 0 for all x in R . Then

Consider the quadratic function f(x)=ax^(2)+bx+c ; a,b,c in R, a!=0 and satisfying the following conditions (i) f(x-4)=f(2-x) AA x in R and f(x)>=x AA x in R (ii) f(x) (iii) Minimum value of f(x) is zero One of the root of the equation f(x)=0 is alpha then 2alpha is equal to

For any real number b, let f (b) denotes the maximum of |sin x+(2)/(3+sin x)+b|AA x in R. Then the minimum vlaue of f (b) AA b in R is:

If f(x) = ax^2 + bx + c and f(0) = 5 , f(1) = 7 , and f(-1) = 3 then find the value of 3a+5b-c .

Let f(b) be the minimum value of the expression y=x^(2)-2x+(b^(3)-3b^(2)+4)AA x in R . Then, the maximum value of f(b) as b varies from 0 to 4 is

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+b^(2))x^(2)+2bx+1 and let m(b) be the minimum value of f(x). As b varies,the range of m(b) is [0,} b.(0,(1)/(2)) c.(1)/(2),1 d.(0,1]

Let f(x)=(1+b^(2))x^(2)+2bx+1 and let m(b) the minimum value of f(x) as b varies, the range of m(b) is (A) [0,1](B)(0,(1)/(2)] (C) [(1)/(2),1](D)(0,1]

Let f(x)=ax^(2)+bx+c, if a>0 then f(x) has minimum value at x=