Question

If zeroes of x3-3x2+x+1 are alpha-beta, alpha and alpha+beta find alpha and beta

Answer 1

Hello dear user ...

Solution here ✌
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By using relationship between the zeros of the Polynomial-

we have

$sum \: \: of \: \: zeroes = \frac{ - ( - coefficient \: \: of \: x)}{coefficient \: \: of \: \: {x}^{2} } \\ \\ = > a - b + a + a + b = \frac{ - ( - 3)}{1} \\ = > 3a = 3 \\ = > a = \frac{3}{3} = 1 \\ \\ and \\ \\ product \: \: of \: the \: \: zeroes = \frac{constant \: \: term}{coefficient \: \: of \: \: {x}^{2} } \\ \\ = > (a - b)(a)(a + b) = \frac{ - 1}{1} \\ = > (1 - b)(1)(1 + b) = - 1 \\ = > 1 - {b}^{2} = - 1 \\ = > {b}^{2} = 2$
=> b -±√2

THEREFORE ,

a = 1. and b± √2

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HOPE it's helps you.
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