Questions
Let three quadratic equations and , all have only positive roots. Then which of these are always true?
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By Expert Faculty of Sri Chaitanya
a
b2 = ac
b
c2 = ab
c
each pair of equations has exactly one root common
d
each pair of equations has two roots common
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Correct option is A
For each equation, required conditions(i) Discriminant≥0⇒b2≥ac,c2≥ab,a2≥bc(ii) f(0)>0 ⇒c,a,b>0(iii) Abscissa of vertex > 0 ⇒ba>0,cb>0,ac>0.Now, b2≥ac,c2≥ab⇒b2c2≥a2bc⇒bc≥a2But a2≥bc. So, a2=bc.Similarly, b2 = ac and c2 = ab.Therefore, a = b = c.
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