Let `Delta(x)=|(x^2-1,x+1,x-2),(2x^2-1,3x,3x-3),(x^2+4,2x-1,2x-1)|.` Prove, by using calculus, that `Delta(x)` is a first degree polynomial.

Let Delta=|{:(,1,x,x^(2)),(,x^(2),1,x),(,x,x^(2),1):}| ,then

Let Delta=|{:(,1,x,x^(2)),(,x^(2),1,x),(,x,x^(2),1):}| . Then

Let f(x) denote the departement f(x)=|{:(x^2,2x,1+x^2),(x^2+1,x+1,1),(x,-1,x-1):}| on expansion f(x) is sen to be a 4th degree polynomial given by f(x)=a_0x^4+a_1x^3+a_2x^2+a_3x+a_4 Using defferentiation of otherwise, match the values of the uantities on the left to those on the right.

If |(x^2+x,x+1,x-2),(2x^2+3x-1,3x,3x-3),(x^2+2x+3,2x-1,2x-1)|=ax-12 then 'a' is equal to (1) 12 (2) 24 (3) -12 (4) -24

If |(x^2+x,x+1,x-2),(2x^2+3x-1,3x,3x-3),(x^2+2x+3,2x-1,2x-1)|=ax-12 then 'a' is equal to (1) 12 (2) 24 (3) -12 (4) -24

If |(x^2+x,x+1,x-2),(2x^2+3x-1,3x,3x-3),(x^2+2x+3,2x-1,2x-1)|=ax-12 then 'a' is equal to (1) 12 (2) 24 (3) -12 (4) -24

Let Delta(x,y)=|(1,x,y),(1,x+y,y),(1,x,x+y)| Then Delta(-3,2) equals

Let x="cos"(pi)/3+i "sin"(pi)/3 and Delta=|(1,x,x^(2)),(x^(2),1,x),(1,x^(2),1)| the numerical value of Delta is

Suppose a epsilon R and x!=0 . Let Delta (x)=|(1-x,a,a^(2)),(a,a^(2)-x,a^(3)),(a^(2),a^(3),a^(4)-x)| Number of values of x which Delta(x)=0 is