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

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

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

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