Last updated at June 15, 2021 by Teachoo
Transcript
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, โ7, โ14 respectively. For a cubic Polynomial p(x) = ax3 + bx2 + cx + d With zeroes ฮฑ, ๐ฝ and ฮณ We have ๐ + ๐ฝ + ๐ = (โ๐)/๐ ๐"๐ฝ" + ๐ฝ๐ + ๐๐ = ๐/๐ ๐"๐ฝ" ๐= (โ๐ )/๐ Let cubic polynomial be p(x) = ax3 + bx2 + cx + d Sum of zeroes Sum of zeroes = 2 (โ๐)/๐ = 2 Assuming a = 1 (โ๐)/1 = 2 b = โ2 Sum of product of zeroes Sum of product of zeroes = โ7 ๐/๐ = โ7 Assuming a = 1 ๐/1 = โ7 c = โ7 Product of zeroes Product of zeroes = โ14 (โ๐)/๐ = โ 14 ๐/๐ = 14 Assuming a = 1 ๐/1 = 14 d = 14 Thus, a = 1, b = โ2 , c = โ7, d = 14 Hence, our cubic polynomial is p(x) = ax3 + bx2 + cx + d = x3 โ 2x2 โ 7x + 14
Ex 2.4 (Optional)
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