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# Exercise 3.3: Polynomials with Additional Information

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EXERCISE 3.3

1. Solve the cubic equation : 2x3 - x2 -18+ 9 = 0 if sum of two of its roots vanishes.

2. Solve the equation 9x3 - 36x2 + 44-16 = 0 if the roots form an arithmetic progression.

3. Solve the equation 3x3 - 26x2 + 52- 24 = 0 if its roots form a geometric progression.

4. Determine and solve the equation 2x3 - 6x2 + 3= 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 - 39+135 , if it is known that1+ 2and âˆš3 are two of its zeros.

6. Solve the cubic equations : (i) 2x3 - 9x2 +10= 3 , (ii) 8x3 - 2x2 - 7+ 3 = 0.

7. Solve the equation : x4 -14x2 + 45 = 0.

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12th Mathematics : UNIT 3 : Theory of Equations : Exercise 3.3: Polynomials with Additional Information | Problem Questions with Answer, Solution

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