If the equation a(b-c)x2+b(c-a)x+c(a-b)=0 has equal roots, where a+c=15 and b= 365, then a2+c2 is equal to .
117
Sum of coefficients =0 x=1 is a root; the roots are equal, so both are 1.
Product of roots = c(a-b)a(b-c)=1 2ac=b(a+c)= 365 15=108 ac=54
a2+c2=(a+c)2-2ac=225-108=117
Answer: 117
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