# PRACTICE PROBLEMS OF SOLVING POLYNOMIAL EQUATIONS

## About "Practice Problems of Solving Polynomial Equations"

Practice Problems of Solving Polynomial Equations

Here we are going to see some example problems of solving cubic with additional information of roots.

## Practice Problems of Solving Polynomial Equations - Practice questions

(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.        Solution

(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 that 1 + 2i an3 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

After having gone through the stuff given above, we hope that the students would have understood, "Practice Problems of Solving Polynomial Equations".

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