Let `f(x)=a^2+b x+c` where a ,b , c in ` Ra n da!=0.` It is known that `f(5)=-3f(2)` and that 3 is a root of `f(x)=0.` then find the other of `f(x)=0.`

Let f(x) be a quadratic polynomial satisfying f(2) + f(4) = 0. If unity is one root of f(x) = 0 then find the other root.

Let f(x) be a quadratic expression such that f(-1)+f(2)=0 . If one root of f(x)=0 is 3 , then the other root of f(x)=0 lies in (A) (-oo,-3) (B) (-3,oo) (C) (0,5) (D) (5,oo)

Given that f'(x)=4x^(3)-3x^(2)+2x-1 find f(x) if f(0)=0 .

If f(x+f(y))=f(x)+yAAx ,y in Ra n df(0)=1, then find the value of f(7)dot

Let f(x)=a sin x+c , where a and c are real numbers and a>0. Then f(x)lt0, AA x in R if

If f(x)=x^3+b x^2+c x+da n df(0),f(-1) are odd integers, prove that f(x)=0 cannot have all integral roots.

Let f(x)=a x^2+b x+c be a quadratic expression having its vertex at (3, -2) and value of f(0)=10. find f(x)

f(x)=|a x-b|+c|x|AAx in (-oo,oo), where a >0, b >0,c > 0. Find the condition if f(x) attains the minimum value only at one point.

Let f(x) = 2x + 5. If x ne 0 then find (f (x +2) - f(2))/(x)

Let f(x)=2x+5 . If xne0 then find (f(x+2)-f(2))/(x)