let f(x) = x3-3x+b and g(x) = x2+bx-3,where b is a real number .what is the sum of all possible values of b for which the equations f(x)=0 and g(x)=0 have a common root
plzz give a detailed solution.
Suppose that the common root is x1, then x1^3 - 3x1 + b = 0 ...... (1), and x1^2 + bx1 - 3 = 0 ..... (2).
Multiply equation (2) by x1 and subtract the resulting equation from equation (1).
That gets you b(1 - x1^2) = 0, so either b = 0 or x1 = + or - 1.
Substitute the x1 values into (2) and calculate the corresponding values of b.
You should find that he sum of the three possible values for b is zero.