The values of a for which `(a^2-1)x^2+2(a-1)x+2` is positive for all real x are

The least integral value of 'k' for which (k-1) x ^(2) -(k+1) x+ (k+1) is positive for all real value of x is:

The minimum value of 'a' for which a^(2)x^(2)+(2a-1)x+1 is non-negative for any real x is __________

Find the values of 'a' for which -3<(x^2+ax-2)/(x^2+x+1)<2 is valid for all real x.

Find the values of 'a' for which -3<(x^2+ax-2)/(x^2+x+1)<2 is valid for all real x.

Find the values of 'a' for which -3<(x^2+ax-2)/(x^2+x+1)<2 is valid for all real x.

Find the values of 'a' for which -3<(x^2+ax-2)/(x^2+x+1)<2 is valid for all real x.

Find the values of 'a' for which -3<(x^(2)+ax-2)/(x^(2)+x+1)<2 is valid for all real

The least integral value of 'k' If (k-1) x ^(2) -(k+1) x+ (k+1) is positive for all real value of x is:

Find the value of a for which a x^2+(a-3)x+1 < 0 for at least one positive real x .

Find the value of a which makes the expression x^2-ax+1-2a^2 always positive for real values of x.