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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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.