Find the cubic polynomial which sum of its zeroes , sum of its product of its zeroes take two at time and product of its zeroes as 2, -7 and -14 respectively
Answers
Answered by
57
Answer:
Step-by-step explanation:
Let the zeroes of the cubic polynomial be α, β and γ respectively.
According to the question ;
Sum of zeroes = 2
⇒ α + β + γ = 2
Sum of the product of the roots taken two at a time = - 7
⇒ αβ + βγ + γα = - 7
Product of zeroes = - 14
⇒ αβγ = - 14
Now, we know that -
The cubic polynomial is given by -
⇒ x³ - (α + β+γ)x² + (αβ + βγ+αγ)x - αβγ
⇒ x³ - 2x² - 7x - 14
Hence, the required cubic polynomial is (x³ - 2x² - 7x - 14).
Anonymous:
Nice :)
Answered by
134
Solution :-
Let α , β and y be be the zeroes of the cubic polynomial.
Given :-
- Sum of zeroes = 2
» α+β+y = 2
- Sum of product of zeroes = -7
» αβ + βy + αy = -7
- Product of zeroes = -14
» αβy = -14
_______________________________
We know that :-
» x³ -( α+β+y)x² +(αβ+βy+αy)x -αβy
_____________________[Put value]
» x³ - (2)x² + (-7)x - (-14)
» x³ - 2x² - 7x+ 14
_______________[Answer]
So, the cubic polynomial is x³ - 2x² - 7x +14
_______________________________
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