Answer:
x + 8
Step-by-step explanation:
x + 5 + 3.
add the numbers
↓
x + 8
To create a survey and hand them out to different students
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:
1/3 I think I did the math and if that's not right try 1/3:1/4 (<--ratio)
Step-by-step explanation:
Answer:
{-1.7, 3.5}
Step-by-step explanation:
I find it convenient to graph the difference of the two sides of the equation. That difference is zero when the equation is satisfied. This equation has two solutions, near x = -1.7 and x = 3.5.
