Largest integral value of m for which the quadratic expression `y=x^(2)+(2m+6)x+4m+12` is always positive `AA x in R` 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

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:

Largest integral value of 'a' for which the expression y=x^(2)+ax+(a-3) is non positive x in[0,1] is

The least integral value of 'm' for which the expression mx^(2)-4x+3m+1 is positive for every x in R is: 1 b.-2 c.-1 d.2

Let f(x)=(1+m)x^2-2(1+3m)x+4(1+2m). Numbe of interval values of m for which given qudratic expression is always positive is (A) 8 (B) 7 (C) 8 (D) 9

The number of integral values of alpha for which the quadratic expression alpha x^(2)+|2 alpha-3|x-6 is positive for exactly two integral values of x is equal to

The quadratic equation x^(2) - (m -3)x + m =0 has

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

The quadratic expression ax^(2)+bx+c>0 AA x in R ,then