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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} - 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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