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Question

Form a cubic polynomial having sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes are 2, -7 and -14 respectively.

JEE/Engineering Exams
Maths
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Let the cubic polynomial be ax3 + bx2 + cx + d ....... (1) Let a, ß, y be the zeroes of the required cubic polynomial, then a+B+y = 5: «B+BY+ ya =-; and aßy = Now, according to the question, a +B+y=2 -d a aß +By+ya=-==-=-7 And apy=-14 --14, -14 Ifa= 1, then b=-2,c=-7, d=14 Substituting the values of a, b, c and d in (i), we get the required cubic polynomial x3 – 2x2 - 7x + 14 This polynomial satisfies all the given conditions
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