Solve :

(a + b)²x² - (a + b)x - 6 = 0; a + b ≠ 0.

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.