If `(x)=|a_1+x b_1+x c_1+x a_2+x b_2+x c_2+x a_3+x b_3+x c_3+x|` , show that `^(x)=0` and that`(x)=(0)+S x ,w h e r eS` denotes the sum of all the cofactors of all the element in `(0)dot`

If f(x) = |(a_1+x, b_1+x, c_1+x), (a_2+x, b_2+x, c_2+x),(a_3+x, b_3+x, c_3+x)| , show that f''(x)=0 and that f(x)=f(0)+S ,where S denotes the sum of all the cofactors of all the element in f(0)dot

If f(x) = |(a_1+x, b_1+x, c_1+x), (a_2+x, b_2+x, c_2+x),(a_3+x, b_3+x, c_3+x)| , show that f''(x)=0 and that f(x)=f(0)+S ,where S denotes the sum of all the cofactors of all the element in f(0)dot

if Delta (x)= |{:(a_(1)+x,,b_(1)+x,,c_(1)+x),(a_(2)+x,,b_(2)+x,,c_(2)+x),(a_(3)+x,,b_(3)+x,,c_(3)+x):}| then show that Delta (x)=0 and that Delta (x)=Delta(0)+sx. where s denotes the sum of all the cofactors of all the elements in Delta (0)

If a_1x+b_1y+c_1z=0, a_2x+b_2y+c_2z=0, a_3x+b_3y+c_3z=0 and |(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)|=0 , then the given system then

Consider the determinant "Delta"=|a_1+b_1x^2a_1x^2+b_1c_1a_2+b_2x^2a_2x^2+b_2c_2a_3+b_3x^2a_3x^2+b_3c_3|0, w h e r ea_i ,b_i , c_i R(1,2,3)a n dx Rdot Statement 1: The value of x satisfying "Delta"=0 are x=1,-1. Statement 2: If |a_1b_1c_1a_2b_2c_2a_3b_3c_3|=0,t h e n"Delta"=0.

a_1, a_2, a_3, in R-{0} and a_1+a_2cos2x+a_3sin^2x=0 for all x in R , then

a_1, a_2, a_3, in R-{0} and a_1+a_2cos2x+a_3sin^2x=0 for all x in R , then

a_1, a_2, a_3, in R-{0} and a_1+a_2cos2x+a_3sin^2x=0fora l lx in R , then