Paragraph: Let f(x), g(x) and h(x) be function of degree more than 5 and (x) (x)= | array ccc x f(x)+f^ ( ) & x g(x)+g^ ( ) & x h(x)+h^ ( ) -2 f( )+3 f^ ( ) & -2 g( )+3 g^ ( ) & -2 h( )+3 h^ ( ) f^ ( ) & g^ ( ) & h^ ( ) array | Question: If

Question

Paragraph: Let f(x), g(x) and h(x) be function of degree more than 5 and (x) (x)= | array ccc x f(x)+f^ ( ) & x g(x)+g^ ( ) & x h(x)+h^ ( ) -2 f( )+3 f^ ( ) & -2 g( )+3 g^ ( ) & -2 h( )+3 h^ ( ) f^ ( ) & g^ ( ) & h^ ( ) array | Question: If f(x), g(x), h(x) are even function (x) will not give remainder 0 when divided by

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Correct answer: D. none of these

By applying R₁ R₁-R₃, R₂ R₂-3 R₃ (x)=-2 x | array lll f(x) & g(x) & h(x) f( ) & g( ) & h( ) f^ ( ) & g^ ( ) & h^ ( ) array | Clearly ( )=0, ^ ( )=0 As f , g , h are function (- )=0, ^ (- )=0 Means (x) has factors x,(x- )^2,(x- )^2

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