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17. Find a cubic polynomial with sum of ts zeroes is 5sum of theprodcts of ts aeroes taken beat a time is-7 and product of its zeroes is- 4 |
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Answer» Let α, β and ɣ be the roots of the cubic polynomial Given (α + β + ɣ) = 5/2(αβ+ βɣ + ɣα) = - 7 and (αβɣ) = - 4 The cubic polynomial with roots α, β and ɣ is x^3 - (α + β + ɣ)x^2 + (αβ+ βɣ + ɣα)x - (αβɣ) = 0 x^3 - (5/2)x^2 + (- 7)x - (- 4) = 0 2x^3 - 5x^2 - 14x + 8 = 0 |
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