If a, b, c are distinct real numbers, then the quadratic expression ((x-b)(x-c)/(a-b)(a-c))+((x-c)(x-a)/(b-c)(b-a))+((x-a)(x-b)/(c-a)(c-b)) is identically equal to

Question

If a, b, c are distinct real numbers, then the quadratic expression ((x-b)(x-c)/(a-b)(a-c))+((x-c)(x-a)/(b-c)(b-a))+((x-a)(x-b)/(c-a)(c-b)) is identically equal to (A) 1 (B) x (C) x2 (D) none of these

Tardigrade Admin · Accepted Answer

Use the fact that expression becomes equal to 1 for x=a, b, c.

Q. If $a, b, c$ are distinct real numbers, then the quadratic expression $\frac{( x - b ) ( x - c )}{( a - b ) ( a - c )} + \frac{( x - c ) ( x - a )}{( b - c ) ( b - a )} + \frac{( x - a ) ( x - b )}{( c - a ) ( c - b )}$ is identically equal to

1

$x$

$x^{2}$

none of these

Use the fact that expression becomes equal to 1 for $x = a, b, c$ .

Q. If a,b,c are distinct real numbers, then the quadratic expression (a−b)(a−c)(x−b)(x−c)​+(b−c)(b−a)(x−c)(x−a)​+(c−a)(c−b)(x−a)(x−b)​ is identically equal to

1

x

x2

none of these

Use the fact that expression becomes equal to 1 for x=a,b,c.

Q. If $a, b, c$ are distinct real numbers, then the quadratic expression $\frac{( x - b ) ( x - c )}{( a - b ) ( a - c )} + \frac{( x - c ) ( x - a )}{( b - c ) ( b - a )} + \frac{( x - a ) ( x - b )}{( c - a ) ( c - b )}$ is identically equal to

$x$

$x^{2}$

Use the fact that expression becomes equal to 1 for $x = a, b, c$ .