
parameter. As an example, we can write a = b + 3, and then choose any value we like for b.Ifb = 0,
we obtain the polynomial Pð x Þ= 3x
2
− 1. Clearly, this is only one of infinitely many possibilities.
40. As b
a
will be a negative number, b must be negative. Indeed powers of positive numbers are alway s
positive. Moreover, a cannot be an even number, because an even exponent generates a positive
result. The numbers a and b can be either fractions or integer numbers.
Let us try b = −27 and a = 1/3. Then a
b
= ð1/3Þ
−27
= 3
27
, which is a positive integer number, and
b
a
= ð−27Þ
1/3
= −3, which is a negative integer.
41. We can consider two cases: either a
n
> 0o ...