Question

$\purple{Any \: Maths \: Aryabhatta}$
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$\huge\colorbox{cyan}{Question}$

${If \: one \: of \: the \: zeroes \: of \: the \: cubic \: polynomial \: x3 + ax² + bx + c \:is \: -1, \: then \: the \: product \: of \: the \: other \: two \: zeroes \: is}$

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Answer 1

is}If one ofthe zero of the cubic polynomial x3+ax²+bx+cis 1

Answer

Answer:

Let α,β be the other zeros of the given polynomial

$x {}^{3} +ax {}^{2} +bx {}^{2} +c$

$sum \: of \: the \: zero = \frac{ - coefficient \: of \: {x}^{2} }{coefficient \: of \: {x}^{3} }$

$= > - 1 + \alpha + \beta = \frac{ - a}{1 } = - a$

$\alpha + \beta = - a + 1$

Again,

$( - a) + \alpha \beta - \beta = \frac{b}{1}$

$= > \alpha \beta = b + a + \beta$

$\alpha + \beta = b + a + \: 1$

$= > b - a + 1$