If the equation a(b-c)x^2 + b(c-a)x + c(a-b) = 0 has equal roots and if a + c = 5 and b = 16/5, then the value of a^2+c^2 is equal to

Question

If the equation \(a(b-c) x^2+b(c-a) x+c(a-b)=0\) has equal roots and if a + c = 5 and \(b=\frac{16}{5},\) then the value of \(a^2+c^2\) is equal to

Answer 1

Answer is "9" 

Clearly 1 satisfy \(\Rightarrow\) other root is also 1 . 

\(\Rightarrow \frac{c(a-b)}{a(b-c)}=1\) (using product of roots)  

\(\Rightarrow c(a-b) = a(b-c)\)