Show that the equation `sintheta=x+1/x` is not possible if `x` is real.

Show that the equation sec^2 theta=(4xy)/(x+y)^2 is only possible when x=y

Show that sin^(2)x=p+1/p is impossible if x is real.

Show that the equation x^(2)+5x-6=0 has real roots.

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

Show that the equation x^2+a x-4=0 has real and distinct roots for all real values of a .

If roots of the equation 2x^2-4x+2sintheta-1=0 are of opposite sign, then theta belongs

The equation "sin" theta = x +(p)/(x) for real values of x is possible when

A quadratic trinomial P(x)=a x^2+b x+c is such that the equation P(x)=x has no real roots. Prove that in this case equation P(P(x))=x has no real roots either.

Show that the function f defined by f(x)=|1-x+x|, where x is any real number, is a continuous function.

Statement -1 : If x is real and y = (x^(2) -x+3)/(x+2) , " then " y in (-oo,oo) - (-11,1) Statement -2 : If [] represents the greatest integer function and f(x) =x -[x] then number of real roots of the equation f(x) +f (1/x)=1 are infinite. Statement -3 : if the difference of the roots of the equation x^(2)+hx +7=0 is 6, then , possible value (s) of h are -8 and 8.