If `x^2 -1 =0` is a factor of `a x^4 + b x^3 + c x^2+dx +e`; show that `a+c+e = b+d =0`

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

If x^(2)-1 is a factor of ax^(4)+bx^(3)+cx2+dx+e, Show that a+c+e=b+d=0

If x+a is a factor of x^(4)-a^(2)x^(2)+3x-6a then a=0( b) -1( c) 1 (d) 2

If x-a is a factor of x^(3)-3x^(2)a+2a^(2)x+b then the value of b is 0(b)2(c)1(d)3

If +-2,quad 3 are the roots of ax^(4)+bx^(3)+cx^(2)+dx+e=0 then the roots of a(x-1)^(3)+b(x-1)^(2)+c(x-1)+d=0

Let |x2xx^2x6xx6|=a x^4+b x^3+c x^2+dx+edot Then, the value of 5a+4b+3c+2d+e is equal 0 (b) -16 (c) 16 (d) none of these

In a A B C , D and E are points on the sides A B and A C respectively such that D E B C If A D=8x-7, D B=5x-3, A E=4x-3 and E C=(3x-1) , find the value of x . (ii) If A D=4x-3, A E=8x-7, B D=3x-1 and C E=5x-3 , find the volume x . (iii) If A D=2. 5 c m , B D=3. 0 c m and A E=3. 75 c m , find the length of A C .

In a A B C , D and E are points on the sides A B and A C respectively such that D E B C If A D=2 c m , A B=6 c m and A C=9 c m , find A E . (ii) If (A D)/(B D)=4/5 and E C=2. 5 c m , find A E . (iii) If A D=x , D B=x-2 , A E=x+2 and E C=x-1 , find the value of x .

Let |x^2+3xx-1x+3x+1-2xx-4x-3x+4 3x|=a x^4+b x^3+c x^2+e be an identity in x , where a , b , c , d , e are independent of xdot Then the value of e is 4 (b) 0 (c) 1 (d) none of these

Differentiate the following functions with respect to x (a) x^(4) + 3x^(2) -2x (b) x^(2) cos x (c) (6x +7)^(4) (d) e^(x) x^(5) (e) ((1 + x))/(e^(x))