`x_1,x_2`are roots of the equation `x^2 + x + c = 0 ,c=! 0`, and `x_1 ^3 /(2+x_2) + x_2 ^3 /(2+x_1) =-1/2` the value of `-4c` is

x_(1),x_(2) are roots of the equation x^(2)+x+c=0,c=10, and (x_(1)^(3))/(2+x_(2))+(x_(2)^(3))/(2+x_(1))=-(1)/(2) the value of -4c

If a, b,c , d are the roots of the equation : x^(4) + 2x^(3) + 3x^(2) + 4x + 5 = 0 , then 1 + a^(2) + b^(2) + c^(2) + d^(2) is equal to :

x_1 and x_3 are the roots of the equation Ax ^2 - 4x +1=0 and x_2 and x_4 =0 are the roots of the requation Bx^2 - 6x + 1=0 if x_1 , x_2 , x_3 ,x_4 form a H.P , then (A,B) =

Let the equation x^(5) + x^(3) + x^(2) + 2 = 0 has roots x_(1), x_(2), x_(3), x_(4) and x_(5), then find the value of (x_(2)^(2) - 1)(x_(3)^(2) - 1)(x_(4)^(2) - 1)(x_(5)^(2) - 1).

Let x_1,x_2,x_3,x_4 ,be the roots (real or complex) of the equation x^4+ax^3+bx^2+cx+d=0 . If x_1+x_2=x_3+x_4 and a,b,c,d in R, then If a=2, then the value of b-c is

x_1 and x_2 are the roots of a x^2+b x+c=0 and x_1x_2<0. Roots of x_1(x-x_2)^2+x_2(x-x_1)^2=0 are: (a) real and of opposite sign b. negative c. positive d. none real

x_1 and x_2 are the roots of a x^2+b x+c=0 and x_1x_2<0. Roots of x_1(x-x_2)^2+x_2(x-x_1)^2=0 are: (a) real and of opposite sign b. negative c. positive d. non real

If a, b, c, d are the roots of the equation x^(4) - 100x^(3)+2x^(2)+4x+10=0 , then the value of (1)/(a)+(1)/(b)+(1)/(c)+(1)/(d) is