If the equation `ax^2 + bx + c = 0` is not altered when each of the coefficient is increased by the same quantity then `x^2+x + 1`=

Each root of the equation ax^2 + bx + c = 0 is decreased by 1. The quadratic equation with these roots is x^2 + 4x + 1 = 0 . The numerical value of b + c is……………….

Find the coefficients of x^(6) in the expansion of (ax^(2) + bx + c)^(9)

Write true or false , The coefficient of x^(0) in the given equation x^(2)+bx+(1)/(c)=0 is c.

If the equations 2x^(2)7x+1=0 and ax^(2)+bx+2=0 have a common root,then

If the equations 2x^(2)-7x+1=0 and ax^(2)+bx+2=0 have a common root, then

If a root of the equation ax^(2)+bx+c=0 be reciprocal of a root of the equation a'x^(2)+b'x+c'=0 then

If the roots of the equation ax^2-bx-c=0 are changed by same quantity then the expression in a,b,c that does not change is