Determine the value of 'a' so that the expression `x^(2)-2(a+1)x+4, x in R` is always positive.

Find what values of a so that the expression x^(2)-(a+2)x+4 is always positive.

(i) Find the values of 'a' for which the expression x^(2)-(3a-1)x+2a^(2)+2a-11 is always positive (ii) If x^(2)+4ax+2 gt0 for all values of x, then a lies in the interval. (a) (-2,4) (b) (1,2) (c) (-sqrt(2),sqrt(2)) (d) (-(1)/(sqrt(2)),(1)/(sqrt(2))) (e) (-4,2).

Determine the sign of the expression i) x^(2)+x+1 ii) -x^(2)+x-1 for x in R .

The number of negative intergral values of m for which the expression x ^(2) + 2(m -1) x +m +5 is positive AA x gt 1 is:

The number of integral values of m for which the quadratic expression (1 + 2m)x^(2) - 2(1 + 3m)x + 4(1 + m), x in R , is always positive is

For what real values of a, will the expression x^(2)-ax+1-2a^(2) , for the real x, be always positive ?

The maximum value of the expression (x^(2)+x+1)/(2x^(2)-x+1) , for x in R , is

The least integral value of lambda for which the expression (lambdax^(2)-4x+3lambda+1) is positive for all x in R,is

The minimum value of the expression 2 ^(x) + 2 ^(2x +1) + (5)/(2 ^(x)) ,x in R is :

Which of the following statements are true regarding the expression f(x)= 2x^(2)+4x+9 ? I. The expression has a least value of 7 II. The value of the expression is always positive for any value of x III. The roots of f(x)=0 are irrational