please answer my questions tennetiraj sir
Answers
EXPLANATION.
α, β, γ are the zeroes of the polynomial.
As we know that,
⇒ α + β + γ = 2. - - - - - (1).
⇒ αβ + βγ + αγ = -7. - - - - - (2).
⇒ αβγ = -14. - - - - - (3).
As we know that,
Formula of cubic polynomial.
⇒ x³ - (α + β + γ)x² + (αβ + βγ + αγ)x - αβγ.
Put the values in the equation, we get.
⇒ x³ - (2)x² + (-7)x - (-14).
⇒ x³ - 2x² - 7x + 14.
Option [C] is the correct answer.
MORE INFORMATION.
Conjugate roots.
(1) = If D < 0.
One roots = α + iβ.
Other roots = α - iβ.
(2) = If D > 0.
One roots = α + √β.
Other roots = α - √β.
Answer:
Option C
Step-by-step explanation:
Given :-
α, β, γ are the zeres and α+ β+γ = 2 ,
αβ+βγ+αγ = -7
α β γ = -14
To find :-
Find the cubic Polynomial ?
Solution :-
Given that :
α, β, γ are the zeres and
α+ β+γ = 2 ,
αβ+βγ+αγ = -7
α β γ = -14
We know that
The cubic Polynomial whose zeroes are α, β, γ is
K[x^3-(α+ β+γ)x^2+(αβ+βγ+αγ)x-α β γ ], Where K is a positive real number
On Substituting these values in the above Polynomial
=> K[x^3-(2)x^2+(-7)x-(-14)]
=> K[x^3-2x^2-7x+14]
If K = 1 then the required Polynomial is
x^3-2x^2-7x+14
Answer:-
The Cubic Polynomial for the given problem is
x^3-2x^2-7x+14
Used formulae:-
- The standard cubic Polynomial is ax^3+bx^2+cx+d .
- The cubic Polynomial whose zeroes are α, β, γ is
- K[x^3-(α+ β+γ)x^2+(αβ+βγ+αγ)x-αβγ]
- Sum of the zeroes = -b/a
- Sum of the product of two zeroes taken at a time = c/a
- Product of the zeroes = -d/a
- The cubic Polynomial has at most three zeroes .