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Find a cubic polynomial with the sum, sum of the product of it's zeroes taken two at a time ,and the product of it's zeroes as 2,-7,-14 respectively. |
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Answer» Let α, β and ɣ be the ROOTS of the cubic polynomial GIVEN (α + β + ɣ) = 2 (αβ+ βɣ + ɣα) = – 7 and (αβɣ) = –14 The cubic polynomial with roots α, β and ɣ is x3 – (α + β + ɣ)x2 + (αβ+ βɣ + ɣα)x – (αβɣ) = 0 ⇒ x3 – (2)x2 + ( – 7 )x – ( – 14) = 0 ⇒ x3 – 2x2 – 7x + 14 = 0 |
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