Let `f(x)=|[1,1,1] , [3-x,5-3x^2,3x^3-1] , [2x^2-1,3x^5-1,7x^8-1]|` then the equation of `f(x)=0` has

Let f(x) =|{:(1,1,1),(3-x,5-3x^(2),3x^(3)-1),(2x^(2)-1,3x^(5)-1,7x^(8)-1):}| then the equation f(x) =0 has

Let f(x)=|(1,1,1),(3x-x,5-3x^(2),3x^(3)-1),(2x^(2)-1,3x^(5)-1,7x^(8)-1)| . Then which of the following is/are correct?

If f(x)=x^3+3x^2+6x+2sinx then the equation 1/(x-f(1))+2/(x-f(2))+3/(x-f(3))=0 has

Let f(x)= x^3+3x^2+6x+2sinx , then the equation 1/(x-f(1))+2/(x-f(2))+3/(x-f(3))=0 ,has

if f(x)=|[x-3,2x^2-18,3x^3-81],[x-5,2x^2-50,4x^3-500],[1,2,3]| then f(1)f(3)+f(3)f(5)+f(5)f(1) is equalto

if f(x)=|[x-3,2x^2-18,3x^3-81],[x-5,2x^2-50,4x^3-500],[1,2,3]| then f(1)f(3)+f(3)f(5)+f(5)f(1) is equal to

If f(x)=[[x-3 , 2 x^2-18 , 3 x^3-81],[ x-5 , 2 x^2-50 , 4 x^3-500],[ 1 , 2 , 3 ]] then f(1) . f(3)+f(3) . f(5)+f(5) . f(1)=

Let f(x)=|(1,3,5),(x-2,3x^(2)-12,5x^(3)-40),(x-3,3x^(2)-27,2x^(3)-54)| then f(2)f(3)+f(2)f(7)+f(3)f(7)= __________

If f(x)=2x^(2)+3x-5 , then prove that f'(0)+3f'(-1)=0