Question

According to the rational root theorem, which of the following are possible roots of the polynomial function below? (Select all that apply)

f(x) = x⁴ - 29x²+ 100
a) 2
b) -2
c) 5
d) -5
e) 10

Answer 1

The possible roots of the polynomial function are: 2, -2, 5, -5, and 10.

Step-by-step explanation:

The given polynomial function is f(x) = x⁴ - 29x² + 100. To find the possible roots of the function using the rational root theorem, we need to consider the factors of the leading coefficient, 1, and the constant term, 100, and form all possible fractions of the form p/q, where p is a factor of 100 and q is a factor of 1.

In this case, the possible roots are:

• a) 2: f(2) = 16 - 29(4) + 100 = 0, so 2 is a root.
• b) -2: f(-2) = 16 - 29(4) + 100 = 0, so -2 is a root.
• c) 5: f(5) = 625 - 29(25) + 100 = 0, so 5 is a root.
• d) -5: f(-5) = 625 - 29(25) + 100 = 0, so -5 is a root.
• e) 10: f(10) = 10000 - 29(100) + 100 = 0, so 10 is a root.