Ex 2.4, 2
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.
For a cubic Polynomial
p(x) = ax3 + bx2 + cx + d
With zeroes α, 𝛽 and γ
We have
𝛂 + 𝛽 + 𝛄 = (−𝒃)/𝒂
𝛂"𝛽" + 𝛽𝛄 + 𝛄𝛂 = 𝒄/𝒂
𝛂"𝛽" 𝛄= (−𝒅)/𝒂
Let cubic polynomial be
p(x) = ax3 + bx2 + cx + d
Sum of zeroes
Sum of zeroes = 2
(−𝑏)/𝑎 = 2
Assuming a = 1
(−𝑏)/1 = 2
b = −2
Sum of product of zeroes
Sum of product of zeroes = −7
𝑐/𝑎 = −7
Assuming a = 1
𝑐/1 = −7
c = −7
Product of zeroes
Product of zeroes = −14
(−𝑑)/𝑎 = − 14
𝑑/𝑎 = 14
Assuming a = 1
𝑑/1 = 14
d = 14
Thus,
a = 1, b = –2 , c = –7, d = 14
Hence, our cubic polynomial is
p(x) = ax3 + bx2 + cx + d
= x3 – 2x2 − 7x + 14

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.