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Question Number 90581 by hardylanes last updated on 24/Apr/20

g i v e n t h a t α a n d β a r e r o o t s o f t h e e q u a t i o n

a χ^{2} + b χ + c = 0 . s h o w t h a t λ μ b^{2} = a c {(λ + μ)}^{2}

w h e r e \frac{α}{β} = \frac{λ}{μ}

Answered by maths mind last updated on 24/Apr/20

\Leftrightarrow λ μ \frac{b^{2}}{a^{2}} = \frac{c}{a} {(λ + μ)}^{2} \Leftrightarrow \frac{λ}{μ} . \frac{b^{2}}{a^{2}} = \frac{c}{a} {(\frac{λ}{μ} + 1)}^{2} . . E

{(\frac{b}{a})}^{2} = {(α + β)}^{2}

\frac{c}{a} = α β

E \Leftrightarrow \frac{α}{β} {(α + β)}^{2} = α β {(1 + \frac{α}{β})}^{2} = \frac{α}{β} {(α + β)}^{2} . . T r u e