When roots of polynomials occur in radical form, they occur as two conjugates.
That is,
The conjugate of (a + √b) is (a - √b) and vice versa.
To show that the given conjugates come from a polynomial, we should create the polynomial from the given factors.
The first factor is x - (a + √b).
The second factor is x - (a - √b).
The polynomial is
f(x) = [x - (a + √b)]*[x - (a - √b)]
= x² - x(a - √b) - x(a + √b) + (a + √b)(a - √b)
= x² - 2ax + x√b - x√b + a² - b
= x² - 2ax + a² - b
This is a quadratic polynomial, as expected.
If you solve the quadratic equation x² - 2ax + a² - b = 0 with the quadratic formula, it should yield the pair of conjugate radical roots.
x = (1/2) [ 2a +/- √(4a² - 4(a² - b)]
= a +/- (1/2)*√(4b)
= a +/- √b
x = a + √b, or x = a - √b, as expected.
Answer:
The result is 
units.
Step-by-step explanation:
The coordinates for A and B:
A = (-2, 0)
B = (2, 2)
-To find the distance between A and B, you need the distance formula:
Where the first coordinate is 
and the second coordinate is 
.
-Use the coordinates A and B for the equation:
-Then, you solve the equation:
So, therefore the distance is 
units.
Answer:
39 points
Step-by-step explanation:
Your school's football team scored 49 points.
Your team's score is 19 points more than the opponents score
The opponent score is represented as S
Since the total points that was scored is 49 and your team score is 19 then the equation can be written as follows
S+ 19= 49
Solve for S
S= 49-19
S= 30
Hence the opponent's score is 30 points
