(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given that the roots of [itex]x^2+px+q=0[/itex] are [itex]\alpha and \beta[/itex], form an equation whose roots are [itex]\frac{1}{\alpha} and \frac{1}{\beta}[/itex]

b) Given that [itex]\alpha[/itex] is a root of the equation [itex]x^2=2x-3[/itex] show that

i)[itex]\alpha^3=\alpha-6[/itex]

ii)[itex]\alpha^2-2\alpha^3=9[/itex]

2. Relevant equations

[tex]\sum\alpha=\frac{-b}{a}[/tex]

[tex]\sum\alpha\beta=\frac{c}{a}[/tex]

3. The attempt at a solution

well for part a) I can do that simply

but it is part b) that confuses me, as I can simply factorize what the eq'n and get 1 and -3 as the roots..but I don't see how i can use those numbers to prove what they want to show...

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# Homework Help: Simple roots of a quadratic question

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