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Let the roots ofx^{2}+x+ 1 = 0 be [itex]\alpha[/itex] and [itex]\beta[/itex], form a quadratic equation with roots:

(i) [itex]\alpha[/itex]^{2}, [itex]\beta[/itex]^{2}; and

(ii) [itex]\frac{1}{\alpha}[/itex], [itex]\frac{1}{\beta}[/itex].

The attempt at a solution

sum of roots = [itex]\alpha[/itex] + [itex]\beta[/itex] = -1

product of roots = [itex]\alpha\beta[/itex] = 1

(i)

sum of roots = [itex]\alpha[/itex]^{2}+ [itex]\beta[/itex]^{2}= (-1)^{2}- 2(1) = -1

product of roots = [itex]\alpha[/itex]^{2}[itex]\beta[/itex]^{2}= 1^{2}= 1

Quadratic equation:x^{2}+x+ 1 = 0

(ii)

sum of roots = [itex]\frac{1}{\alpha}[/itex] + [itex]\frac{1}{\beta}[/itex] = [itex]\frac{-1}{1}[/itex] = -1

product of roots = ([itex]\frac{1}{\alpha}[/itex])([itex]\frac{1}{\beta}[/itex]) = 1

Quadratic equation:x^{2}+x+ 1 = 0

Is this weird? Did I do something wrong?

Thanks.

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# Homework Help: Forming a quadratic equation

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