# FIND A CUBIC POLYNOMIAL WITH THE GIVEN ZEROS WORKSHEET

Construct a cubic equations with roots

Problem 1 :

1, 2 and 3

Solution

Problem 2 :

1, 1 and -2

Solution

Problem 3 :

2, 1/2 and 1

Solution

Problem 4 :

If the sides of a cubic box are  increased by 1, 2, 3 units respectively to form a cuboid then the volume is increased by 52 cubic units. Find the volume of the cuboid.

Solution

1)  x3 - 6x2 + 11x - 6 = 0

2)  x3 - 3x + 2 = 0

3)  2x3 - 7x2 + 7x - 2 = 0

4)  60 cubic units.

If α, β and γ are the roots of the cubic equation

x3 + 2x2 + 3x + 4 = 0

form a cubic equation whose roots are

Problem 1 :

2α, 2β and 2γ

Solution

Problem 2 :

1/α, 1/β and 1/γ

Solution

Problem 3 :

-α, -β and -γ

Solution

1)  x3 - 4x2 + 12x - 32 = 0

2) 4x3 + 3x2 + 2x + 1 = 0

3)  x3 - 2x2 + 3x - 4 = 0

Find all cubic polynomials with zeros of :

Problem 1 :

±2, 3

Solution

Problem 2 :

-2, ± i

Solution

Problem 3 :

3, -1 ± i

Solution

Problem 4 :

-1, -2 ± √2

Solution

1)  a(x2 - 4) (x - 3).

2)  a(x2 - 4) (x - 3).

3) a(x - 3) (x2 + 2x + 2)

4) a(x + 1) (x2 + 4x + 2)

Problem 1 :

Find all the zeroes of the polynomial x3 + 3x2 – 2x – 6, if two of its zeroes are -√2 and √2.

Solution

Problem 2 :

Find all the zeroes of the polynomial 2x3 + x2 – 6x – 3, if two of its zeroes are -√3 and √3.

Solution

Problem 3 :

Obtain all other zeroes of the polynomial 2x3 - 4x – x2 + 2, if two of its zeroes are √2 and -√2.

Solution

Problem 4 :

If the polynomial 6x4 + 8x3 + 17x2 + 21x + 7 is divided by another  polynomial 3x2 + 4x + 1 then the remainder comes out to be ax + b, find ‘a’ and ‘b’.

Solution

1) All the zeroes are -√2, √2 and -3

2)  All the zeroes are -√3, √3 and -1/2.

3)  All the zeroes are - √2, -√2 and 1/2.

4)  All the zeroes are -√3, √3 and -1/2.

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