Answer:
We want a polynomial of smallest degree with rational coefficients with zeros in
,
and -3. The last root gives us the factor (x+3). Hence, our polynomial is

where
is a polynomial with rational coefficients and roots
and
. The root
gives us a factor
, but in order to obtain rational coefficients we must consider the factor
.
An analogue idea works with
. For convenience write
. This gives the factor
. Hence,

Notice that
. So, in order to satisfy the last condition we divide by 3 the whole polynomial, without altering its roots. Finally, the wanted polynomial is

Step-by-step explanation:
We must have present that any polynomial it's determined by its roots up to a constant factor. But here we have irrational ones, in order to eliminate the irrational coefficients that a factor of the type
will introduce in the expression, we need to multiply by its conjugate
. Hence, we will obtain
that have rational coefficients. Finally, the last condition is given with the intention to fix the constant factor. Usually it is enough to evaluate in the point and obtain the necessary factor.
Answer:
x=0,
y=0
Step-by-step explanation:

Answer:
if you're trying to find the discriminant, then it's 181.
Step-by-step explanation:
Answer:

Step-by-step explanation:
We have the right triangle. The sum of the angles measured in the right triangle is 90 °. Therefore we have the equation:
<em> add 10 to both sides</em>
<em>divide both sides by 10</em>

The measure of angles:
Put the value of x to the eqpressions:

<span>F is the midpoint of EG
so EF = FG = 5
EG = EF + FG = 5 + 5 = 10
</span>
EH = EF + FH = 5 + 11 = 16
answer
EH = 16