If α and β are roots of the equation $$x2$$−$$3x+a=0$$ and γ and δ are roots of the equation $$x2$$−$$12x+b=0$$ and α,β,γ,δ form an increasing GP, then the values of a and b are respectively

Question

If α and β are roots of the equation $$x2$$−$$3x+a=0$$ and γ and δ are roots of the  equation $$x2$$−$$12x+b=0$$ and α,β,γ,δ form an increasing  GP, then the values  of a and b are respectively

Infinity Learn · Accepted Answer

∵α,β,γ,δ are in GP.Let α$$=A$$,β$$=Ar$$,γ$$=Ar2$$,δ$$=Ar3$$∵α and β are the roots of the equation $$x2$$−$$3x+a=0$$,then  γ$$+$$δ$$=12$$⇒$$Ar2(1+r)=12$$ ....(ii)On$$ solving Eqs. $$(i) and (ii), we get    $$A=1$$,$$r=2$$⇒    α$$=1$$,β$$=2$$,γ$$=4$$,δ$$=8$$∴    $$a=$$αβ$$=1$$×$$2=2$$ and     $$b=$$γδ$$=4$$×$$8=32$$

If $α$ and $β$ are roots of the equation $x^{2} - 3 x + a = 0$ and $γ$ and $δ$ are roots of the equation $x^{2} - 12 x + b = 0$ and $α, β, γ, δ$ form an increasing GP, then the values of a and b are respectively

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If α and β are roots of the equation x2−3x+a=0 and γ and δ are roots of the equation x2−12x+b=0 and α,β,γ,δ form an increasing GP, then the values of a and b are respectively

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Ready to Test Your Skills?

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If $α$ and $β$ are roots of the equation $x^{2} - 3 x + a = 0$ and $γ$ and $δ$ are roots of the equation $x^{2} - 12 x + b = 0$ and $α, β, γ, δ$ form an increasing GP, then the values of a and b are respectively