If `(x^2+a x+3)//(x^2+x+a)` takes all real values for possible real values of `x ,` then a.`4a^2+39<0` b. `4a^5+39 >-0` c. `ageq1/4` d. `a<1/4`

H(x) increase as f(x) decreases for all real values of x if

If x is real and (x^2+2x+c)//(x^2+4x+3c) can take all real values, of then show that 0lt=clt=1.

Let f(x)=a x^2+b x+a ,b ,c in Rdot If f(x) takes real values for real values of x and non-real values for non-real values of x , then a=0 b. b=0 c. c=0 d. nothing can be said about a ,b ,cdot

Let sqrt(((x+1)(x-3))/((x-2))) . Find all the real values of x for which y takes real values.

If |x^2- 2x- 8| + |x^2+ x -2|= 3|x +2| , then the set of all real values of x is

Find all possible values of (x^2+1)/(x^2-2) .

Let y=sqrt(((x+1)(x-3))/((x-2))) . Find all the real values of x for which y takes real values.

If A = sin^2x + cos^4 x , then for all real x :

For all real values of x, the minimum value of (1-x+x^(2))/(1+x+x^(2)) is

Prove that for all real values of xa n dy ,x^2+2x y+3y^2-6x-2ygeq-11.