F4 maths Quadratic equations

Could anyone help me with these questions?


1) If x = k (x-1)(x-4) has two identical roots, find the values of k.

2) If the graph of y = x^2 + (k+1)x +4 touches the x-axis,
a) Find the two values of k,
b) Hence find the x-intercept for each case.

3) If 3z^2 + 6z + p + 1 = 0 has real roots, find the maximum value of p.

4) Find the value of k if the roots of 3x^2 + (k+3)x - 12 = 0 are numerically equal but opposite in sign.

5) Find the value of p if one root of 3x^2 - 4x + p = 0 is three times the other.

Thankssss!!!!