if `x_1 , x_2` are the roots of `ax^2+bx+c=0` , find the value of `(1) (ax_1 +b )^-2 + (ax_2 +b )^-2 (2) (ax_1 +b )^-3 + (ax_2 +b)^-3`

If 1,2,3 and 4 are the roots of x^4+ax^3+bx^2+cx+d=0 , then find the values of a,b,c and d.

If x=1/3 , -1 are the roots of the equation ax^2+bx-1=0 ,find a and b.

If x_(1),x_(2) are the roots of the quadratic equation ax^(2)+bx+c=0 and c ne 0, find the value of (ax_(1)+b)^(-2)+(ax_(2)+b)^(-2) in terms of a,b,c

If (x-1)^(2) is a factor of ax3+bx2+c, find the value of a+b+c

If a and b ( != 0) are roots of x^(2) +ax + b = 0 , then the least value of x^(2) +ax + b ( x in R) is :

If (x+1) and (x-1) are factor of ax^(3) + bx^(2) + 3x+5 . Find the value of a and b

If x-1 is a factor of 2x^(3)+ax^(2)+2bx+1 and 2a-b=4 . Find the values of a and b.

If a and b are the non-zero distinct roots of x^(2) + ax + b =0 , then the minimum value of x^2 + ax + b is