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Class 10
Mathematics
Polynomials
find a cubic polynomial with the sum sum of the p...

Question:
Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, –7, –14 respectively.

Answer:

Let the p(x) = ax³+bx²+ cx + d

Sum of zeroes and α, β and γ be the zeroes.

Then, α, β and γ = -b/ a = 2/1 …………………..(i)

αβ + βγ + γα= c/a = -7 …………………….(ii)

‘ αβγ = -d /a = -14 ……………………………..(iii)

From equation (i), (ii) and (iii), we get

a = 1, b = -2, c = -7 and d = 14

Therefore, the required polynomial on putting the value of a, b, c and d is P(x) = x³ - 2x² – 7x + 14

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Question:
Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, –7, –14 respectively.

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Question: Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, –7, –14 respectively.

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Question:
Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, –7, –14 respectively.