If `(x^2+p x+1)` is a factor of `(a x 63+b x+c),t h e n` `a^2+c^2=-a b` b. `a^2-c^2=-a b` c. `a^2-c^2=a b` d. none of these

If (x^2+p x+1) is a factor of (a x^3+b x+c),t h e n a. a^2+c^2=-a b b. a^2-c^2=-a b c. a^2-c^2=a b d. none of these

If (x^2+p x+1) is a factor of (a x^3+b x+c),t h e n a^2+c^2=-a b b. a^2-c^2=-a b c. a^2-c^2=a b d. none of these

If x^2+p x+1 is a factor of the expression a x^3+b x+c , then a^2-c^2=a b b. a^2+c^2=-a b c. a^2-c^2=-a b d. none of these

If x^2+p x+1 is a factor of the expression a x^3+b x+c , then a^2-c^2=a b b. a^2+c^2=-a b c. a^2-c^2=-a b d. none of these

If x^2+p x+1 is a factor of the expression a x^3+b x+c , then a^2-c^2=a b b. a^2+c^2=-a b c. a^2-c^2=-a b d. none of these

If x^2-1 is a factor of a x^4+b x^3+c x^2+dx+e , show that a+c+e=b+d

If x^2-1 is a factor of a x^4+b x^3+c x^2+dx+e , show that a+c+e=b+d

If x^2-1 is a factor of a x^4+b x^3+c x^2+dx+e , show that a+c+e=b+d

If f(x)=f(x)={(sin(a+1)x+sinx)/(x), ,x<0,c \ at x=0, (sqrt(x+b x^2)-sqrt(x))/(b xsqrt(x)),xgeq0,f(x) is continuous at x=0,t h e n (a). a=-3/2,b=0,c=1/2 (b) a=-3/2,b=1,c=-1/2 (c) a=-3/2,b in R-[0],c=1/2 (d) none of these

If af(x+1)+bf(1/(x+1))=x ,x!=-1,a!=b ,t h e nf(2) is equal to (a) (2a+b)/(2(a^2-b^2)) (b) a/(a^2-b^2) (c) (a+2b)/(a^2-b^2) (d) none of these