A polynomial g(x) is given by:
g(x) = (x-1)(x+2)(x-a)(x-b)
1) given that a and b are integers, give the possible values for a and b.
Thank you
To find the possible values for the integers a and b in the given polynomial g(x), we can use the zero-factor property. According to this property, if a polynomial is equal to zero, then one or more of its factors must be equal to zero.
In this case, based on the given polynomial g(x), we can set it equal to zero:
g(x) = (x-1)(x+2)(x-a)(x-b) = 0
Now, we can analyze the factors of g(x) and find the possible values for a and b that would make each factor equal to zero.
1) Setting x - 1 = 0, we get x = 1. So, one possibility for a and b is that both are NOT equal to 1.
2) Setting x + 2 = 0, we get x = -2. So, one possibility for a and b is that both are NOT equal to -2.
3) Setting x - a = 0, we get x = a. So, one possibility for a and b is that both are NOT equal to a.
4) Setting x - b = 0, we get x = b. So, one possibility for a and b is that both are NOT equal to b.
Combining all the conditions, we find that to satisfy all the equations, a and b must be integers that are NOT equal to 1, -2, a, and b.
In summary, the possible values for a and b are any integer except for 1, -2, a, and b.