Consider the polynomial p(x) = x^3 + 4x^2 + 6x − 36.
1 answer:
Answer:
a. attached graph; zero real: 2
b. p(x) = (x - 2)(x + 3 + 3i)(x + 3 - 3i)
c. the solutions are 2, -3-3i and -3+3i
Step-by-step explanation:
p(x) = x³ + 4x² + 6x - 36
a. Through the graph, we can see that 2 is a real zero of the polynomial p. We can also use the Rational Roots Test.
p(2) = 2³ + 4.2² + 6.2 - 36 = 8 + 16 + 12 - 36 = 0
b. Now, we can use Briott-Ruffini to find the other roots and write p as a product of linear factors.
2 | 1 4 6 -36
1 6 18 0
x² + 6x + 18 = 0
Δ = 6² - 4.1.18 = 36 - 72 = -36 = 36i²
√Δ = 6i
x = -6±6i/2 = 2(-3±3i)/2
x' = -3-3i
x" = -3+3i
p(x) = (x - 2)(x + 3 + 3i)(x + 3 - 3i)
c. the solutions are 2, -3-3i and -3+3i
You might be interested in
Answer:
Step-by-step explanation:
Given:
Let's changed that mixed number to an improper fraction. Now we get:
Let's find out least common denominator. This one is easy, the LCD is 8. Now that we know the LCD, let's convert both our fractions:
We can use because it is equal to
. Now, all we need to do is subtract the numerators:
Answer:
9 inches
Step-by-step explanation:
The formula for the volume of a rectangular pyramid is
- Here we have volume (V), base (L), and width (W)
- V = 360 in³, L = 12 in, W = 10 in
We need to manipulate the volume equation to solve for the height (H)
- First we need to multiply both sides by 3 to get rid of the fraction: 3V = L×W×H
- Then we need to divide both sides by (L×W) to get:
Now we can plug in the given values:
- The height is 9 inches
Answer:
when simplified and added this is what i got and when redone too over check i got it again hopefully this helps.