If equation `x^2+2x+2 + e^alpha - 2 sin beta = 0` has a real solution in `x,` then (where `n in ZZ`)

If the equation cos2x+alpha sin x=2 alpha-7 has a solution.Then range of alpha is

If alpha is a real root of the quadratic equation a x^2+b x+c=0a n dbeta ils a real root of -a x^2+b x+c=0, then show that there is a root gamma of equation (a//2)x^2+b x+c=0 whilch lies between alpha & beta

If alpha and beta ( != 0) are the roots of the quadratic equation x^(2) + ax - beta = 0," then the quadratic expression " -x^(2) + alpha x + beta " where " x in R has

The differential equation whose solution is (x - alpha)^(2) + (y - beta)^(2) = a^(2) [ for all alpha " and " beta where a is constant ] of is -

If the equation 2x^(4)+x^(3)-2x-1=0 has two real roots alpha and beta , then between alpha and beta the equation 8x^(3)+3x^(2)-2=0 has -

The equation (cos beta-1) x^(2)+(cos beta) x+sin beta=0 in the variable x has real roots, then beta is in the interval