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)

Let f (x) be a quadratic expressinon which is positive for all real values of x, If g(x)=f(x)+f'(x)+f''(x), then for any real x

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)

If f'(x) = 9 x^(2) - 6 x and f (0) = - 3 , find f(x)

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)=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) =4x^2-4ax+a^2-2a+2 be a quadratic polynomial in x,a be any real number. If x-coordinate of vertex of parabola y =f(x) is less than 0 and f(x) has minimum value 3 for x in [0,2] then value of a is

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

Let f(x)=a x^2+b x+a ,b ,c in Rdot If f(x) takes real values for real values of x and non-real values for non-real values of x , then a=0 b. b=0 c. c=0 d. nothing can be said about a ,b ,cdot