First slide
Theory of equations

Let three quadratic equations ax22bx+c=0,bx22cx+a=0 and cx22ax+b=0, all have only positive roots. Then which of these are always true?


For each equation, required conditions

(i) Discriminant0b2ac,c2ab,a2bc

(ii) f(0)>0 c,a,b>0

(iii) Abscissa of vertex > 0 ba>0,cb>0,ac>0.

Now, b2ac,c2abb2c2a2bcbca2

But a2bc. So, a2=bc.

Similarly, b2 = ac and c2 = ab.

Therefore, a = b = c.

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