Question

State the possible rational roots for each function. Then find all roots.f(x) = 5x3- 21x2- 21x+ 5.

Answer 1

The possible rational roots are ±1, ±5. The function f(x) = 5x^3 - 21x^2 - 21x + 5 has roots x = 1/5, x = -1/5, and x = -1.

Step-by-step explanation:

The possible rational roots can be determined using the rational root theorem. According to the theorem, the possible rational roots are the factors of the constant term (5) divided by the factors of the leading coefficient (5).

So, the possible rational roots are ±1, ±5.

To find all the roots, we can use synthetic division or a graphing calculator. By performing synthetic division with the possible rational roots, we can determine that the function has a root of x = 1/5. Using polynomial long division or a graphing calculator, we can then factor the quadratic result and find the roots x = -1/5 and x = -1.