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AP EAMCET202017 Sep 2020Morning ShiftMathematicsDeterminantsActual

If (f(x)= | array ccc x-3 & 2 x^2-18 & 3 x^3-81 x-5 & 2 x^2-50 & 4 x^3-500 1 & 2 & 3 array | ), then (f( l ) f(3)+f(3) f(5)+f(5) f( l ) ) is equal to

Options

  1. A(f(1) )
  2. B(f(3) )
  3. C(f(1)+f(3) )
  4. D(f(1)+f(5) )

Correct answer

B. (f(3) )

Step-by-step solution

(f(x)=(x-3)(x-5) | array ccc 1 & 2(x+3) & 3 (x^2+9+3 x ) 1 & 2(x+5) & 4 (x^2+25+5 x ) 1 & 2 & 3 array | ) ( f(3)=f(5)=0 ) So, (f(1) f(3)+f(3) f(5)+f(5) f(1)=0=f(3) )

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