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ax-2-bx-c-0-has-roots-and-and-show-that-b-2-ac-2-




Question Number 211815 by alcohol last updated on 21/Sep/24
ax^2 +bx+c=0 has roots α and β  and (α/β)=(λ/μ). show that λμb^2  = ac(λ+μ)^2
ax2+bx+c=0hasrootsαandβandαβ=λμ.showthatλμb2=ac(λ+μ)2
Answered by som(math1967) last updated on 22/Sep/24
 let α=kλ , β=kμ   k(λ+μ)=−(b/a)  ⇒k^2 (λ+μ)^2 =(b^2 /a^2 )   k^2 =(b^2 /(a^2 (λ+μ)^2 ))   again k^2 λμ=(c/a)  ⇒ ((b^2 λμ)/(a^2 (λ+μ)^2 ))=(c/a)  ∴λμb^2 =ac(λ+μ)^2
letα=kλ,β=kμk(λ+μ)=bak2(λ+μ)2=b2a2k2=b2a2(λ+μ)2againk2λμ=cab2λμa2(λ+μ)2=caλμb2=ac(λ+μ)2

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