Question

find a cubic Polynomial with the sum of the
Product of its zero taken two at a
time and product of its Zeroes as 3-1
and 3 respectively .​

Answer 1

Answer:

4cube 64. ....

cubic polynomial .............

Answer 2

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[ 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]

= k[x³ - (α + β + γ)x² + (αβ+βγ+αγ)x - αβγ]Given :

= 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 - (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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