Question

Which of the following are possible rational roots of the polynomial function f(x)=5x^2-3x+3

Answer 1

You didn't post any option, but the ration roots theorem states that all possible rational roots of a polynomial come in the form

$\pm\dfrac{p}{q}$

where p divides the constant term and q divides the leading term of the polynomial. So, in your case, p divides 3 (i.e. it is 1 or 3), and q divides 5 (i.e. it is 1 or 5).

So, the possible roots are

$\pm 1,\quad \pm 3,\quad \pm\dfrac{1}{5},\quad \pm\dfrac{3}{5}$

For the record, this parabola has no real roots.

Answer 2

Answer:

Step-by-step explanation: