Answer:
The potential real zeros are \(\pm 1,\pm 3, \pm \frac{1}{2},\pm \frac{3}{2}, \pm \frac{1}{4}, \pm \frac{3}{4}\).
Step-by-step explanation:
The given polynomial is
\(f(x)=4x^5-16x^4+17x^3-19x^2+13x-3=0\)
According to the rational root theorem, all the potential real zeros are in the form of
\(r=\pm \frac{p}{q}\)
Where, p is the factor of constant and q is the factor of leading coefficient.
The constant term is -3 and leading coefficient is 4.
Factors of -3 are ±1, ±3.
Factors of 4 are ±1, ±2, ±4.
The potential real zeros are
\(\pm 1,\pm 3, \pm \frac{1}{2},\pm \frac{3}{2}, \pm \frac{1}{4}, \pm \frac{3}{4}\)
Therefore potential real zeros are \(\pm 1,\pm 3, \pm \frac{1}{2},\pm \frac{3}{2}, \pm \frac{1}{4}, \pm \frac{3}{4}\).
