Question

find a cubic polynomial whose zeroes are -2,5,1 upon 3

Answer 1

Hey dear !!!

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==> In the example,

We have given that,

-2 , 5 and 1/3 are the zeroes of the unknown polynomial.

We have to find the the required cubic polynomial .

Let, α = -2 , β = 5 and γ = 1/3

We Know that,

Sum of zeroes = α + β + γ

∴ α + β + γ = -2 + 5 + 1/3

= -6 + 15 + 1/3

= 9 + 1/3

= 10/3

∴ α + β + γ = 10/3

We also know that,

Product of zeroes = αβ + βγ + γα

∴ αβ + βγ + γα = -2(5)+5(1/3) + 1/3(-2)

= -10 + 5/3 + (-2/3)

= -30 + 5 - 2/3

= -25 - 2/3

= -27/3

= -9

∴ αβ + βγ + γα = -9

Also,

αβγ = -2(5)(1/3)

= -10(1/3)

= -10/3

∴ αβγ = -10/3

The required cubic polynomial is .

x³- ( α + β + γ)x² + (αβ +βγ + γα)x - (αβγ)

x³ - 10/3x² + (-9)x - (-10/3)

x³ - 10/3x² - 9x + 10/3

Therefore, the required cubic polynomial is [ x³ - 10/3x² - 9x + 10/3 ]

Thanks !!!

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