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3 years ago

Explain one of the theorems that you would use to find the zero of higher degree polynomial

1 answer:

8 0

The zeros of a function f(x) are the values of x that cause f(x) to be equal to zero
One of methods to find the zeros of polynomial functions is The Factor Theorem

It is used to analyze polynomial equations. By it we can know that there is a relation between factors and zeros.

let: f(x)=(x−c)q(x)+r(x)

If c is one of the zeros of the function , then the remainder r(x) = f(c) =0
and f(x)=(x−c)q(x)+0 or f(x)=(x−c)q(x)

Notice, written in this form, x – c is a factor of f(x)
the conclusion is: if c is one of the zeros of the function of f(x),
then x−c is a factor of f(x)

And vice versa , if (x−c) is a factor of f(x), then the remainder of the Division Algorithm f(x)=(x−c)q(x)+r(x) is 0. This tells us that c is a zero for the function.

So, we can use the Factor Theorem to completely factor a polynomial of degree n into the product of n factors. Once the polynomial has been completely factored, we can easily determine the zeros of the polynomial.

You might be interested in

What is 76.3 rounded to the nearest whole number

MatroZZZ [7]

76.
If the number after the decimal is below five, you round down. If the number is above five, you round up. 76 is your answer.

6 0

3 years ago

You're standing on the ground 7777 meters away from the bottom of a tall tower. The tower itself is 346346 meters tall. What is

lys-0071 [83]

Answer:

88.7°

Step-by-step explanation:

First, visualize. Assuming that the tower is at a perfectly 90° angle to the ground, you have a right triangle. We will call this triangle ΔABC where A is where you are, B is the top of the tower, and C is the base of the tower. Now we know the following:

∠A = ?

∠B = ?

∠C = 90

a = 346346

b = 7777

c = ?

Note: Triangles are labeled with three pairs of letters: a, b and c and A, B and C. The lower case letters, a, b and c represent the sides, and the upper case letters are the angles that are directly opposite of those sides. (see attached reference)

c is easy, c is the hypotenuse, so you can use the following equation to find the hypotenuse:

a² + b² = c²

Rearranged:

c = ± $\sqrt{a^{2} +b^{2} }$

Substitute a and b:

c = ± $\sqrt{346346^{2} +7777^{2} }$

Comes out to ~346433.3 meters.

Now if we use the Law of Sines:

$\frac{a}{sinA}$ = $\frac{b}{sinB}$ = $\frac{c}{sinC}$

We can use c and a, since we're trying to find what angle A is, so the ratio is set up as:

$\frac{346346}{sinA}$ = $\frac{346433.3}{sinC}$

Well we know that C = 90, and so sin(90) in degrees (as opposed to radians) is 1. So then the set of equations is now:

$\frac{346346}{sinA}$ = $\frac{346433.3}{1}$

Cross Multiply to get rid of the fractions:

346346 = 346433.3 * sin(A)

Divide:

$\frac{346346}{346433.3}$ = sin(A)

Using a calculator, if you take the arcsin of that fraction, you will get what angle A is supposed to be:

arcsin( $\frac{346346}{346433.3}$ ) = ∠A = 88.7°

5 0

2 years ago

Identify the equation of a line in slope-intercept form that is perpendicular to y = -1/3 x + 2 and passes through (2, 1)

Airida [17]

Answer:

Step-by-step explanation:

The slope of a line perpendicular to another line is the opposite reciprocal of the slope of the other line, meaning if the slope of the other line is $-\frac{1}{3}$ , then the slope of the line perpendicular is $3$ .