Question

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

Answer 1

We substitute both and simplify the equations:

9+3a+b=0

1-a+b=0

to solve the prior equations together we multiply the second equation by 3 and add it to the first one and we get:

12+3b=0

3b=-12

b=-12/3

We replace b with -4 and get the answer for a:

1-a-4=0

a=-3