The determinant `"Delta"=|a^2+x a b a c a bb^2+x b c a c b cc^2+x|` is divisible by `x` b. `x^2` c.`x^3` d. none of these

the determinant Delta=|[a^2+x, ab, ac] , [ab, b^2+x, bc] , [ac, bc, c^2+x]| is divisible by

The determinant Delta=|{:(a^(2)+x^(2),ab,ac),(ab,b^(2)+x^(2),bc),(ac,bc,c^(2)+x^(2)):}| is divisible by

The determinant Delta = |(a^(2) + x^(2),ab,ac),(ab,b^(2) + x^(2),bc),(ac,bc,c^(2) + x^(2))| is divisible

The determinant Delta=|{:(,a^(2)(1+x),ab,ac),(,ab,b^(2)(1+x),(bc)),(,ac,bc,c^(2)(1+x)):}| is divisible by

If a , b , c are real numbers, then find the intervals in which f(x)=|x+a^2a b a c a b x+b^2b c a c b c x+c^2| is increasing or decreasing.

If f(x)=|x+a^2a b a c a b x+b^2b c a c b c x+c^2|,t h e n prove that f^(prime)(x)=3x^2+2x(a^2+b^2+c^2)dot

If x+y+z=0 prove that |a x b y c z c y a z b x b z c x a y|=x y z|a b cc a bb c a|

If f(x)=det[[a,-1,0ax,a,-1ax^(2),ax,a]], then f(2x)-f(x) is divisible by (a) a(b)b(c)c,d,e(d) none of these