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Question Number 93129 by 16091019 last updated on 11/May/20
derive x^2 −(α+β)x+αβ
$${derive}\:{x}^{\mathrm{2}} −\left(\alpha+\beta\right){x}+\alpha\beta \\ $$
Commented by 16091019 last updated on 11/May/20
Commented by i jagooll last updated on 11/May/20
(x−α)(x−β)  done
$$\left(\mathrm{x}−\alpha\right)\left(\mathrm{x}−\beta\right) \\ $$$$\mathrm{done} \\ $$
Answered by Rio Michael last updated on 11/May/20
any quadratic with roots α and β   is of the form  (x−α)(x−β) = 0  ⇒ x^2 −(α +β)x + αβ = 0 done!
$$\mathrm{any}\:\mathrm{quadratic}\:\mathrm{with}\:\mathrm{roots}\:\alpha\:\mathrm{and}\:\beta\: \\ $$$$\mathrm{is}\:\mathrm{of}\:\mathrm{the}\:\mathrm{form}\:\:\left({x}−\alpha\right)\left({x}−\beta\right)\:=\:\mathrm{0} \\ $$$$\Rightarrow\:{x}^{\mathrm{2}} −\left(\alpha\:+\beta\right){x}\:+\:\alpha\beta\:=\:\mathrm{0}\:\mathrm{done}! \\ $$

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