1. Solve the cubic equation : 2x3 - x2 -18x + 9 = 0 if sum of two of its roots vanishes.
2. Solve the equation 9x3 - 36x2 + 44x -16 = 0 if the roots form an arithmetic progression.
3. Solve the equation 3x3 - 26x2 + 52x - 24 = 0 if its roots form a geometric progression.
4. Determine k and solve the equation 2x3 - 6x2 + 3x + k = 0 if one of its roots is twice the sum of the other two roots.
5. Find all zeros of the polynomial x6 - 3x5 - 5x4 + 22x3 - 39x2 - 39x +135 , if it is known that1+ 2i and âˆš3 are two of its zeros.
6. Solve the cubic equations : (i) 2x3 - 9x2 +10x = 3 , (ii) 8x3 - 2x2 - 7x + 3 = 0.
7. Solve the equation : x4 -14x2 + 45 = 0.