For roots r1 and r2, the factors are (x-r1)(x-r2)
r1=i
r2=-i
don't forget i^2=-1
(x-i)(x-(-i))=(x-i)(x+i)=x^2-i^2=x^2-(-1)=x^2+1
the function is
f(x)=x^2+1
Answer:
area 78.54cm² circumference 31.42cm
Step-by-step explanation:
to find the circumference you multiply the radius by two, to find the area use the equation A=πr2=π·52 to get 78.53982cm² which is simplified to 78.54cm²
The polynomial equation is f(x) = (x + 1)(x - 1)(x - 7)(x + 2)
<h3>How to determine the polynomial equation?</h3>
The given parameters are
- Degree of polynomial = 4
- Zeros of the polynomial = -1, 1 and 7
- Constant term = 14
The sum of multiplicities of the polynomial equation must be equal to the degree.
This means that the multiplicity of each zero is 1
The equation of the polynomial is then calculated as
P(x) = (x - zero)^ multiplicity
So, we have
P(x) = (x + 1)(x - 1)(x - 7)(x - a)
Recall that
Constant term = 14
This means that
P(0) = 14
So, we have
(0 + 1)(0 - 1)(0 - 7)(0 - a) = 14
Evaluate
7(0 - a) = 14
Divide by 7
0 - a = 2
So, we have
a = -2
Substitute a = -2 in P(x) = (x + 1)(x - 1)(x - 7)(x - a)
P(x) = (x + 1)(x - 1)(x - 7)(x + 2)
Rewrite as
f(x) = (x + 1)(x - 1)(x - 7)(x + 2)
Hence, the equation of the polynomial equation is f(x) = (x + 1)(x - 1)(x - 7)(x + 2)
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It's 8, -8 i think. Square root 64 = ± 8
<u>The expression that represents the volume of </u><u>the cone is 6aπ.</u>
What is called cone?
- A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the center of base) called the vertex.
- The volume of a cone is expressed as;
- V = (1/3)πr²h
- Where r is the radius, h is height and π is pie
Given the data in the question;
Radius r = 3
Height h = 2a
Volume of the cone V = ?
We substitute our given values into the expression above.
V = (1/3) × π × r² × h
V = (1/3) × π × (3)² × 2a
V = (1/3) × π × 9 × 2a
V = 18aπ / 3
V = 6aπ
Therefore, the expression that represents the volume of the cone is 6aπ.
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