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Question

Consider a2(x−b)(x−c)(a−b)(a−c)+b2(x−c)(x−a)(b−c)(b−a)+c2(x−a)(x−b)(c−a)(c−b)=x2, then which of the following is/are true

A
Given equation is an identity
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B
a,b,c are the roots of the given equation
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C
Given equation is not an identity
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D
Roots of the given equation are equal
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Solution

The correct options are
A Given equation is an identity
B a,b,c are the roots of the given equation
a2(xb)(xc)(ab)(ac)+b2(xc)(xa)(bc)(ba)+c2(xa)(xb)(ca)(cb)=x2
By observation,
x=a,x=b,x=c satisfy the given equation.
a,b,c are the roots
and there are 3 roots which is greater than the degree of the given equation.
It is a identity.

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