if α , β are the roots of the quadratic equation ax^2 +bx+c =0 then find the quadratic equation whose roots are α^(2 ) , β^2


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Question Number 37139 by nishant last updated on 09/Jun/18

$i f α, β a r e t h e r o o t s o f t h e q u a d r a t i c$ $e q u a t i o n {a x}^{2} + b x + c = 0 t h e n f i n d$ $t h e q u a d r a t i c e q u a t i o n w h o s e r o o t s$ $a r e α^{2}, β^{2}$
	Answered by tanmay.chaudhury50@gmail.com last updated on 09/Jun/18
	$x^2 −x(α^2 +β^2 )+α^2 β^2 =0 x^2 −x{(α+β)^2 −2αβ}+(αβ)^2 =0× x^2 −x{((b^2 /a^2 )−((2c)/a))}+(c^2 /a^2 )=0 a^2 x^2 −x(b^2 −2ac)+c^2 =0$
	$x^{2} - x (α^{2} + β^{2}) + α^{2} β^{2} = 0$ $x^{2} - x {{(α + β)}^{2} - 2 α β} + {(α β)}^{2} = 0 \times$ $x^{2} - x {(\frac{b^{2}}{a^{2}} - \frac{2 c}{a})} + \frac{c^{2}}{a^{2}} = 0$ $a^{2} x^{2} - x (b^{2} - 2 a c) + c^{2} = 0$
	Answered by Joel579 last updated on 09/Jun/18

	$α + β = - \frac{b}{a}, α β = \frac{c}{a}$ $The new quadratic equation :$ $x^{2} - (α^{2} + β^{2}) x + α^{2} β^{2} = 0$ $x^{2} - [{(α + β)}^{2} - 2 α β] x + {(α β)}^{2} = 0$ $x^{2} - (\frac{b^{2}}{a^{2}} - \frac{2 c}{a}) x + \frac{c^{2}}{a^{2}} = 0$ $a^{2} x^{2} - (b^{2} - 2 a c) x + c^{2} = 0$
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