Answer:
If
or
, there is only one solution to the given quadratic equation.
Step-by-step explanation:
Given a second order polynomial expressed by the following equation:

This polynomial has roots
such that
, given by the following formulas:



The signal of
determines how many real roots an equation has:
: Two real and different solutions
: One real solution
: No real solutions
In this problem, we have the following second order polynomial:
.
This means that 
It has one solution if




We can simplify by 8

The solution is:
or 
So, if
or
, there is only one solution to the given quadratic equation.
Answer:

Step-by-step explanation:
step 1
Find the measure of the arc DC
we know that
The inscribed angle measures half of the arc comprising
![m\angle DBC=\frac{1}{2}[arc\ DC]](https://tex.z-dn.net/?f=m%5Cangle%20DBC%3D%5Cfrac%7B1%7D%7B2%7D%5Barc%5C%20DC%5D)
substitute the values
![60\°=\frac{1}{2}[arc\ DC]](https://tex.z-dn.net/?f=60%5C%C2%B0%3D%5Cfrac%7B1%7D%7B2%7D%5Barc%5C%20DC%5D)


step 2
Find the measure of arc BC
we know that
----> because the diameter BD divide the circle into two equal parts
step 3
Find the measure of angle BDC
we know that
The inscribed angle measures half of the arc comprising
![m\angle BDC=\frac{1}{2}[arc\ BC]](https://tex.z-dn.net/?f=m%5Cangle%20BDC%3D%5Cfrac%7B1%7D%7B2%7D%5Barc%5C%20BC%5D)
substitute the values
![m\angle BDC=\frac{1}{2}[60\°]](https://tex.z-dn.net/?f=m%5Cangle%20BDC%3D%5Cfrac%7B1%7D%7B2%7D%5B60%5C%C2%B0%5D)

therefore
The triangle DBC is a right triangle ---> 60°-30°-90°
step 4
Find the measure of BC
we know that
In the right triangle DBC


substitute the values

Answer: 
Step-by-step explanation:

Add
on both sides and subtract
on both sides to leave x's on the left side and independent values on the right.


Solve the fractions.





Convert the mixed fraction
to an improper fraction. You can do this by multiplying 1 times 35 and adding 2.

Now use the reciprocal (inverse fraction) and multiply on both sides to isolate x.



