Question

find a cubic polynomial with the sum sum of the product of its zeros taken two at a time, and the product of its zeros as 3,-1÷2,5÷4 respectively.

Answer 1

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].

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