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

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

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 (a) 1+sqrt2 (b) 1-sqrt2 (c) 1-sqrt3 (d) 1+sqrt3

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 (a) 1+sqrt(2) (b) 1-sqrt(2) (c) 1-sqrt(3) (d) 1+sqrt(3)

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

Let f(x)= 4x^2-4ax+a^2-2a+2 be a quadratic polynomial in x , a in R . If y = f(x) takes minimum value 3 on x ∈ [0, 2] and x-coordinate of vertex is greater than 2, then value of a is (a) 5-sqrt(10) b. 10-sqrt(5) c. 5+sqrt(10) d. 15/(5+sqrt(10))

A polynomial function f(x) is such that f'(4)= f''(4)=0 and f(x) has minimum value 10 at x=4 .Then

A polynomial function f(x) is such that f''(4)= f''(4)=0 and f(x) has minimum value 10 at ax=4 .Then

Let f(x) = 4x^(2)-4ax+a^(2)-2a+2 and the golbal minimum value of f(x) for x in [0,2] is equal to 3 The number of values of a for which the global minimum value equal to 3 for x in [0,2] occurs at the endpoint of interval[0,2] is