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

If f(x) = ax^(2)+bx+c, f(-1)=-18 , and f(1)=10 , what is the value of b ?

If f(x)=ax^(2)+bx+c and f(x+1)=f(x)+x+1 , then the value of (a+b) is __

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

Let f(x) = x^2 + ax + b . If the maximum and the minimum values of f(x) are 3 and 2 respectively for 0 <= x <= 2 , then the possible ordered pair(s) of (a,b) is/are

If f(x)={(sin((2x^2)/a)+cos((3x)/b))^(ab//x^2),x!=0 & e^3 at x=0} is continuous at x=0AAb in R then minimum value of a is -1//8 b. -1//4 c. -1//2 d. 0

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 ?

If f(x) is a cubic polynomial x^3 + ax^2+ bx + c such that f(x)=0 has three distinct integral roots and f(g(x)) = 0 does not have real roots, where g(x) = x^2 + 2x - 5, the minimum value of a + b + c is

Let f(x)=(1+b^2)x^2+2b x+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]