Question

Find all zeros of the function.

f(x)=5x^3-11x^2+7x-1

Answer 1

To find the zeros of the cubic function, we can use synthetic division and factoring techniques.

Step-by-step explanation:

The given function is a cubic function, which means it can have up to three roots or zeros. To find the zeros of the function, we need to solve the equation f(x) = 5x^3 - 11x^2 + 7x - 1 = 0.

1. One way to solve cubic equations is by using synthetic division with potential roots. By testing different values for x, it is determined that x = 1 is a zero of the function.
2. After performing synthetic division with (x-1), we obtain the quotient 5x^2 - 6x + 1.
3. Factoring the quadratic equation 5x^2 - 6x + 1 = 0, we find the remaining two zeros to be x = 1/5 and x = 1.

Therefore, the zeros of the function f(x) = 5x^3 - 11x^2 + 7x - 1 are x = 1, x = 1/5, and x = 1.