[Maximum mark: 5] The cubic equation x' - kx' + 3k =0 where k > 0 has roots a, B and a + B. Given that af = - find the value of k. 4 8820-7201 6. [Maximum mark: 4] Consider the equation ax + bx + c =0, where a # 0. Given that the roots of this equation are x = sin 0 and x = cos 0, show that b' = a + 2ac. - 8 - 2221-7106 7. [Maximum mark: 8] Consider the quartic equation z* + 4z' + 82 + 80z + 400 =0, ze C. Two of the roots of this equation are a + bi and b + ai, where a, be Z. Find the possible values of a