Question 288826
A degree of 5 means the highest exponent in the polynomial is 5. The degree also tells you how many roots/zeros it has.<br>
With rational coefficients, the zeros with square roots will come in conjugate pairs: (p+q) and (p-q). This is true because when you multiply (p+q)(p-q) you get {{{p^2-q^2}}} which is an expression of perfect squares. This means the square roots will disappear (which needs to happen if there are rational coefficients).<br>
You are given one rational zero, 1/2, and two zeros with square roots:
{{{2+sqrt(7)}}}
and
1-3i (Remember that "i" is a square root! It is {{{sqrt(-1)}}}.)
There are 5 zeros in a polynomial of degree 5 so there two missing zeros. They will be the other "half" of the respective conjugate pairs:
{{{2-sqrt(7)}}}
and
1+3i