KCET2024MathematicsDeterminants

Let f(x)= | array ccc x & x & 1 2 x & x & 2 x x & x & x array | . Then, _ x 0 f(x) x^2 is

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Correct answer

B. 0

Step-by-step solution

f(x)= | array ccc x & x & 1 2 x & x & 2 x x & x & x array | array r = x (x^2-2 x^2 )-x(2 x x-2 x x) +1(2 x x-x x) array =-x^2 x+x x Now, _ x 0 f(x) x^2 = _ x 0 ( -x^2 x+x x x^2 )= _ x 0 (- x+ x x )=-1+1 [ _ x 0 x x =1 ]=0

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