Find the cubic polynomial with the sum, sum of the product of its zeros taken two at a time, and product of its zeros as 3, −1 and − 3 respectively.
Answers
SOLUTION :
If α, β ,γ are the three Zeroes of a cubic polynomial then cubic polynomial will be of the form :
=k[ x³ – (sum of the zeroes) x² + (sum of the products of its zeroes) x – (product of the zeroes)]
[k is non-zero real numbers]
= k[x³ - (α + β + γ)x² + (αβ+βγ+αγ)x - αβγ]
Given :
α + β + γ = 3 …………(1)
αβ+βγ+αγ = -1 ………..(2)
αβγ = -3 ………….(3)
x³ - (α + β + γ)x² + (αβ+βγ+αγ)x - αβγ
= x³ - 3x² +(-1)x - (−3)
[From eq 1,2 & 3]
= k[x³- 3x² - x + 3]
[k is non-zero real numbers]
Hence, the cubic polynomial is k[x³- 3x² - x + 3].
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Answer:
Step-by-step explanation:
SOLUTION :
If α, β ,γ are the three Zeroes of a cubic polynomial then cubic polynomial will be of the form :
=k[ x³ – (sum of the zeroes) x² + (sum of the products of its zeroes) x – (product of the zeroes)]
[k is non-zero real numbers]
= k[x³ - (α + β + γ)x² + (αβ+βγ+αγ)x - αβγ]
Given :
α + β + γ = 3 …………(1)
αβ+βγ+αγ = -1 ………..(2)
αβγ = -3 ………….(3)
x³ - (α + β + γ)x² + (αβ+βγ+αγ)x - αβγ
= x³ - 3x² +(-1)x - (−3)
[From eq 1,2 & 3]
= k[x³- 3x² - x + 3]
[k is non-zero real numbers]
Hence, the cubic polynomial is k[x³- 3x² - x + 3].