Question

If a,b,c are distinct positive real numbers such that b(a+c) = 2ac then the roots a$x^2$ + 2bx + c = 0 are :

• A. Real and equal
• B. Real and distinct
• C. Imaginary
• D. None of these

Answer 1

The correct option is C

Imaginary

D= 4$b^2$ -4ac = 4{ 4$\frac{a^2{c}^2}{(a+c{)}^2}$ -ac}

=$\frac{4ac}{(a+c{)}^2}$ {4ac-${(a+c)}^2$ }

= $\frac{-4ac}{(a+c{)}^2}$ *${(a-c)}^2$ $<$0 [ since a,c$>$0]

=> roots are imaginary