PRACTICE PROBLEMS ON SOLVING POLYNOMIAL EQUATIONS

(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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