Roots or Solutions??

Algebra Level 4

Find the number of roots of the equation:

a 2 ( x − b ) ( x − c ) ( a − b ) ( a − c ) + b 2 ( x − c ) ( x − a ) ( b − c ) ( b − a ) + c 2 ( x − a ) ( x − b ) ( c − a ) ( c − b ) = x 2 . a^2\frac{(x-b)(x-c)}{(a-b)(a-c)}+b^2\frac{(x-c)(x-a)}{(b-c)(b-a)}+c^2\frac{(x-a)(x-b)}{(c-a)(c-b)}=x^2.

0 1 2 Infinite

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Sanjeet Raria by Sanjeet Raria , 27, India

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2 solutions

Sanjeet Raria
Sep 17, 2014

In spite of the equation being a quadratic, it's clearly satisfied by three values of x- a, b, c. Hence this is an identity. So it's satisfied by every value of x.

14 Helpful 0 Interesting 0 Brilliant 0 Confused
Sakshi Taparia
Jan 2, 2015

the given equation is an identity in x, meaning it can take any value and the equation will still hold true.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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