Find the values of k, for which the given equation has real roots:

2x² — 10x + k = 0

If the roots of the equation (a — b)x² + (b — c) x + (c — a) = 0 are equal, prove that 2a = b + c.

If — 5 is a root of the quadratic equation 2x² + 2px — 15 = 0 and the quadratic equation p (x² + x) + k = 0 has equal roots, find the value of k.

Find the values of k, for which the given equation has real roots:

kx² — 6x — 2 = 0

Find the values of k, for which the given equation has real roots:

kx²+ 4x + 1 = 0