Prove that `x^(4)+2x^(2)-x+2=0` has no real solution.

Show that (x^2+1)^2-x^2=0 has no real roots.

Find all the values of p for which the equation x^(4)-4x^(3)-8x^(2)+p=0 has two real solutions

if cos^4x+sin^2x-p=0 has real solutions then

49. If [x^2-2x + a] = 0 has no solution then

Show that the equation 2x^(2)-6x+7=0 has no real root.

Find the value of such that x^(3)-|a|x^(2)+ 3x +4 = 0 has only one real root.

Find the range of lambda for which equation x^3+x^2-x-1-lambda=0 has 3 real solution.

The value of 'a' for which the equation 4cosec^(2)pi(a+x)+a^(2)-4a=0 has a real solution is

If b^2<2a c , then prove that a x^3+b x^2+c x+d=0 has exactly one real root.

If equation x^4-(3m+2)x^2+m^2=0(m >0) has four real solutions which are in A.P., then the value of m is______.