An algebra problem by Yash Singh
Algebra
Level
pending
the quadratic equation , (x+b)(x+c)/(b-a)(c-a) + (x+c)(x+a)/(c-b)(a-b) +(x+a)(x+b)/(a-c)(b-c) =1 has
non real complex roots
two equal roots
infinite roots
two real and distinct roots
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1 solution
after solving the equation , the roots are x=-a, x=-b, x=-c in general , quadratic equation can have maximum of two roots . but the given equation 3 roots which is only possible if equation is an identity and we know an identity can have infinite roots . hence the given equation has infinite roots .