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