Final answer:
To find the other roots of the polynomial p(x) = x³ - 2x² - 19x + 20, given that p(5)=0, we factor the polynomial using (x - 5) and find the quadratic factor to solve for the remaining roots.
Step-by-step explanation:
The student has given the polynomial p(x) = x³ - 2x² - 19x + 20 and stated that p(5) = 0, which means that x = 5 is a root of the polynomial.
To find the other roots, we can factor the polynomial. Since x = 5 is a root, we know that (x - 5) is a factor of p(x). We can perform polynomial division or use synthetic division to divide p(x) by (x - 5). This will yield a quadratic factor, which we can then factor or use the quadratic formula to solve for the remaining roots.