Without solving the following quadratic equation, find the value of 'm' for which the given equation has real and equal roots.

x² + 2(m - 1)x + (m + 5) = 0

Find the value of k for which equation 4x² + 8x - k = 0 has real roots.

If -2 is a root of the equation 3x² + 7x + p = 1, find the value of p. Now find the value of k so that the roots of the equation x² + k(4x + k - 1) + p = 0 are equal.

Case study:
An Air India flight from Mumbai to Colombo was delayed by 60 minutes due to emergency landing of the plane in Vizag as a passengers in the flight suddenly had a cardiac arrest. Now to reach destination of 1800 km from Vizag to Colombo in time, so that passengers could catch their connecting flights, the speed of the plane was increased by 300 km/h than the usual speed.

Based on the above information, answer the following questions :

(i) Taking the usual speed of plane as x km/h, form quadratic equation for situation described above.

(ii) Find the nature of the roots of the quadratic equation.

(iii) Find the usual speed of the plane.