Question

Write rhe cubic polynomial whose zeroes are 6,10,4

Answer 1

Heya.


Your answer is here....

Given zeroes are :- 6, 10, and 4.

Sum of the zeroes = α+β+γ
= 6 + 10 + 4 = 20

Sum of the product of the zeroes taken two at a time = αβ+βγ+αγ
= 6 X 10 + 10 X 4 + 4 X 6 = 60 + 40 + 24 = 124

Product of zeroes = αβγ 
= 6 X 10 X 4 = 240.

Using the cubic formula, 

x³ - ( α+β+γ )x² + ( αβ+βγ+αγ )x - αβγ
x³ - (20)x² + (124)x - 240
-> x³ - 20x² + 124x -240 =0

Hence, the cubic polynomial is x³ - 20x² + 124x -240.
Hope it helps ..........

Answer 2

Heya.


This is your answer ..
It is given that the zeroes are 6, 10, and 4.

Using the cubic formula, 

-> x³ - ( α+β+γ )x² + ( αβ+βγ+αγ )x - αβγ
-> x³ - (6 + 10 + 4)x² + (6 X 10 + 10 X 4 + 4 X 6)x - 6 X 10 X 4
-> x³ - (20)x² + (124)x - 240
-> x³ - 20x² + 124x -240 =0

Hence, the required cubic polynomial is x³ - 20x² + 124x -240.

Hope I helped You..