Find for what value of `'a'` equation `x^2 + 2x - (a^3 - 3a - 3) = 0` has real roots.

Find the values of 'm' for which the equation x^4-(m-3)x^2+m =0 has Four real roots

Find the values of 'm' for which the equation x^4-(m-3)x^2+m =0 has No real roots

Without solving, find the values of 'p' for which the equation x^2 + (p -3)x +p = 0 has real and equal roots.

Find all the value of m for which the equation sin^(2)x-(m-3)sin x+m=0 has real roots.

The least +ve integral value of 'a' for which the equation 3x^4 +4x^3-12x^2 +5a=0 has no real root is

Find all the value of m for which the equation sin^2x-(m-3)sinx+m=0 has real roots.

Find all the value of m for which the equation sin^2x-(m-3)sinx+m=0 has real roots.

Find all the value of m for which the equation sin^2x-(m-3)sinx+m=0 has real roots.

Find the value of a if x^(3) - 3x + a = 0 has three distinct real roots.