Answer:
A) - Quartic polynomial
- has four roots
- roots are; f(x) = (x + 5i)(x - 5i)(x + 2)(x - 2)
B) - Cubic polynomial
- has 3 roots
- roots are; f(x) = (x - 5)²(x + 5)
Step-by-step explanation:
A) f(x) = x⁴ + 21x² − 100
The highest power in this polynomial is 4 and thus, it is called a quartic polynomial. This means that it will have 4 roots.
Factorizing this polynomial gives;
f(x) = (x² + 25)(x² - 4)
Equating to zero, we can find the roots. Thus, the roots are;
x = 5i
x = -5i
x = 2
x = -2
Thus, the completely factorized polynomial is;
f(x) = (x + 5i)(x - 5i)(x + 2)(x - 2)
B) f(x) = x³ − 5x² − 25x + 125
The highest power in this polynomial is 3. It is therefore a cubic polynomial with 3 roots.
Factorizing this polynomial gives;
f(x) = (x² - 25)(x - 5)
Equating to zero and Factorizing gives;
x = 5
x = -5
x = 5
Thus, completely factorized with the roots is;
f(x) = (x - 5)²(x + 5)
Answer:
0.1997 or 19.97%
Step-by-step explanation:
Have taken course online (H) = 23%
Have NOT taken course online (N) = 77%
Have taken course online and don't believe they provide same value (H&D) = 61%
Have NOT taken course online and don't believe they provide same value (N&D) = 73%
The probability that a student has taken a course online given that she does not believe that online courses provide the same educational value as one taken in person is;
There is a 0.1997 or 19.97% chance that she has taken an online course before.
Answer:
y=-5/9
Step-by-step explanation:
it says 9y=-5
divide both sides by 9
y=-5/9
Answer:
You would need a total of 3 3/4 cups. First double the amount of butter= 3 cups, then half 1 1/2 cups for the last cup of flour which would be 3/4. Add them together, it would equal 3 3/4 cups.
Step-by-step explanation:
Step-by-step explanation:
Equations such as x + 3 = 7 are first-degree equations, since the variable has an exponent of 1. The terms to the left of an equals sign make up the left-hand member of the equation; those to the right make up the right-hand member. Thus, in the equation x + 3 = 7, the left-hand member is x + 3 and the right-hand member is 7.
