The quadratic expression `x^(2)-x+1` is positive for x

The value of 'a' for which the quadratic expression ax^(2)+|2a-3|x-6 is positive for exactly two integral values of x is

Let f(x) be a quadratic expression which is positive for all ral x and g(x) = f(x) + f'(x) + f''(x), then for any real x,

Let f(x) be a quadratic expression which is positive for all real x and g(x)=f(x)+f'(x)+f''(x) .A quadratic expression f(x) has same sign as that coefficient of x^2 for all real x if and only if the roots of the corresponding equation f(x)=0 are imaginary.Which of the following holds true? (A) g(0)g(1)lt0 (B) g(0)g(-1)lt0 (C) g(0)f(1)f(2)gt0 (D) f(0)f(1)f(2)lt0

The maximum value of the quadratic expression 12x-x^(2)-32 is

The expression a^(2)x^(2)+bx+1 will be positive for all x in R if

(1) The minimum value of the quadratic expression x^(2)+bx+c is (2) if maximum value at x=a then a=