If the roots of the given equation `(cosp-1)x^2+(cosp)x+sinp=0` are real if

If the roots of the quadratic equation x^(2) +2x+k =0 are real, then

If a , b , c , are real, then prove that roots of the equation 1/(x-a) + 1/(x-b) + 1/(x-c) = 0 are real.

Number of real roots of the equation e^(x-1)-x=0 is

Number of real roots of the equation e^(x-1)-x=0 is

If the roots of the equation x^2+2c x+a b=0 are real unequal, prove that the equation x^2-2(a+b)x+a^2+b^2+2c^2=0 has no real roots.

The equation (cosp - 1)x^(2) + (cosp)x + sinp = 0 , where x is a variable, has real roots. Then the interval of p may be any one of the following :

The values of 'a' for which the roots of the equation x^(2) + x + a = 0 are real and exceed 'a' are

The values of 'a' for which the roots of the equation x^(2) + x + a = 0 are real and exceed 'a' are