Respuesta :
You didn't post any option, but the ration roots theorem states that all possible rational roots of a polynomial come in the form
[tex]\pm\dfrac{p}{q}[/tex]
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
[tex]\pm 1,\quad \pm 3,\quad \pm\dfrac{1}{5},\quad \pm\dfrac{3}{5}[/tex]
For the record, this parabola has no real roots.
The possible rational roots of the polynomial function f(x) = 5x² - 3x + 3 are;
±1/5, ±3/5, ±1, ±3
We are given the polynomial function;
f(x) = 5x² - 3x + 3
The rational root theorem states that for a polynomial to have any rational roots, then the roots must be of the form;
±(Factors of coefficient of constant term/factors of the coefficient of the highest power)
Now, the coefficient of the highest power is 5 and the constant term is 3.
Factors of 5 = 1, 5
Factors of 3 = 1, 3
Thus, the possible rational roots are;
±1/5, ±3/5, ±1, ±3
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