Question

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..

Answer 1

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

Answer 2

Heyaaa...

Here's your answer...

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$sum \: of \: zeroes = - b \div a = 2 \\ sum \: of \: product \: of \: zeroes \: takn \: two \: at \: a \: time = c \div a = - 7 \\ product \: of \: zeroes = - d \div a = - 14$
$and \: formula \: for \: cubic \: polynomial \: \\ = {x}^{3} - ( \alpha + \beta ) {x}^{2} + ( \alpha \beta + \beta \gamma + \gamma \alpha )x - \alpha \beta \gamma$
$so \: polynomial \: is \: {x}^{3} - 2 {x}^{2} - 7 {x}^{2} + 14$
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