If f (x) = `|(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0)|`then

Solve |(x+a,b,c),(a,x+b,c),(a,b,x+c)|=0

If a ,b ,c are different, then the value of x for which |[0,x^2-a, x^3-b], [x^2+a,0,x^2+c ],[x^4+b, x-c,0]|=0 is

If f(x)=|[a,-1, 0],[a x, a,-1],[a x^2,a x, a]|,t h e nf(2x)-f(x) is divisible by (a) a (b) b (c) c ,d ,e (d) none of these

f(x) = |{:(x+c_(1),,x+a,,x+a),(x+b,,x+c_(2),,x+a),(x+b,,x+b,,x+c_(3)):}| " and " g(x)= (C_(1) -x)(c_(3)-x) Coefficient of x in f(x) is

f(x) = |{:(x+c_(1),,x+a,,x+a),(x+b,,x+c_(2),,x+a),(x+b,,x+b,,x+c_(3)):}| " and " g(x)= (C_(1) -x)(c_(3)-x) Which of the following is not a constant term in f(x) ?

If f(x)=1/x ,g(x)=1/(x^2), and h(x)=x^2 , then (A) f(g(x))=x^2,x!=0,h(g(x))=1/(x^2) (B) h(g(x))=1/(x^2),x!=0,fog(x)=x^2 (C) fog(x)=x^2,x!=0,h(g(x))=(g(x))^2,x!=0 (D) none of these

Solve for x in R : |((x+a)(x-a),(x+b)(x-b),(x+c)(x-c)),((x-a)^3,(x-b)^3,(x-c)^3),((x+a)^3,(x+b)^3,(x+c)^3)| =0, a,b and c being distinct real numbers.

If g(x)=(f(x))/((x-a)(x-b)(x-c)) ,where f(x) is a polynomial of degree <3 , then intg(x)dx=|[1,a,f(a)log|x-a|],[1,b,f(b)log|x-b|],[1,c,f(c)log|x-c|]|-:|[1,a, a^2],[ 1,b,b^2],[ 1,c,c^2]|+k (dg(x))/(dx)=|[1,a,-f(a)(x-a)^(-2)],[1,b,-f(b)(x-b)^(-2)],[1,c,-f(c)(x-c)^(-2)]|:-|[1,a,a^2],[1,b,b^2],[1,c,c^2]|

If f(x)=a x^2+b x+c ,g(x)=-a x^2+b x+c ,w h e r ea c!=0, then prove that f(x)g(x)=0 has at least two real roots.