According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? f(x) = 8x7 – x5 + x3+6

Answers

Answer 1

Answer: According to the Fundamental Theorem of Algebra, the number of roots of a polynomial is equal to the degree of the polynomial. The degree of the polynomial is the highest exponent of a term in the polynomial.
Looking at the function, the term with the highest exponent is 8x7. The exponent is 7; therefore, the function has 7 roots.

Answer 2

Answer:

According to the Fundamental Theorem of Algebra, the roots exist for the polynomial function $f\left( x \right) = 8{x^7} - {x^5} + {x^3} + 6 x$ is $\boxed7.$

Further explanation:

The Fundamental Theorem of Algebra states that the polynomial has n roots if the degree of the polynomial is n.

$f\left( x \right) = a{x^n} + b{x^(n - 1)} +\ldots + cx + d$

The polynomial function has n roots or zeroes.

Degree is highest power of the polynomial function.

Given:

The polynomial function is $f\left( x \right) = 8{x^7} - {x^5} + {x^3} + 6.$

Explanation:

The polynomial function $f\left( x \right) = 8{x^7} - {x^5} + {x^3} + 6$ has seven zeroes as the degree of the polynomial is 7.

According to the Fundamental Theorem of Algebra, the roots exist for the polynomial function $f\left( x \right) = 8{x^7} - {x^5} + {x^3} + 6$ is $\boxed7.$

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1. Learn more about inverse of the functionbrainly.com/question/1632445.

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Polynomials

Keywords: quadratic equation, equation factorization. Factorized form, polynomial, quadratic formula, zeroes, Fundamental Theorem of algebra, polynomial, seven roots.

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Which value of x is a solution to this equation?2x^2 − 4x +16 = 0

x = 3

x=2

x = -2

Answers

Answer:

Solve the equation:

2x² − 4x + 16 = 0
x² - 2x + 8 = 0
x² - 2x + 1 + 7 = 0
(x - 1)² + 7 = 0
(x - 1)² = -7

There is no solution as the square of the number can't be negative

----------------------------

Note if the equation was 2x² - 4x - 16 = 0, the solution would be:

2x² - 4x - 16 = 0
x² - 2x - 8 = 0
x² - 2x + 1 = 9
(x - 1)² = 3²
x - 1 = ± 3
x = -2, x = 4

In this case x = -2 is the correct choice

Answer:

x = -2

Step-by-step explanation:

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Susan volunteers at her local animal shelter. She counts the dogs and notices that there are a total of 37 dogs. Of those, 24 are female. What percentage of the dogs are male?

Answers

Answer:

35.135% of dogs are males ( approx )

Step-by-step explanation:

Given,

Total dogs = 37,

Also, dogs who are female = 24,

So, the male dogs = 37 - 24 = 13,

Hence, the percentage of male dogs = $\frac{\text{Male dogs}}{\text{Total dogs}}* 100$

$=(13)/(37)* 100$

$=(1300)/(37)$

$=35.135\%$

What are the coordinates of the image produced by applying the composition Ro,-270 degrees o Ro,-90 degrees to the point (–5, 4)?A. (–5, 4)
B. (–4, –5)
C. (4, 5)
D. (5, –4)

Answers

On dealing with a rotation of -270 degrees or 90 degrees (both are equal to each other), it is necessary to know the relation between the x and y coordinates to know the new coordinate points of the rotated image. The rotation relation for a 90 degree rotation is:

R90 (x,y) = (-y , x)

Therefore, with that being applied to the point (-5,4), the new coordinate points of the rotated image would be: (-4,-5). Among the choices, the correct answer is B.

If b = 1/2x −1/y, then what is an expression for 2/b in terms of x and y?

Answers

Final answer:

After rearranging the given formula to put b on one side, we found the reciprocal of b to be 1/b = 2y/(y-2x). Multiplying by 2 gives 2/b = 4y/(y-2x) in terms of x and y.

Explanation:

To find an expression for 2/b in terms of x and y, let's first rearrange the question's provided formula, b = 1/2x - 1/y, to express b on one side of the equation. This rearrangement allows us to then find the reciprocal of b, which is 1/b. Following that, we can multiply 1/b by 2 in order to give us the expression for 2/b.

With our initial formula, b = 1/2x - 1/y, if we multiply each term by 2y, the formula then becomes 2yb = y - 2x. Rearranging this formula gives us b = (y-2x)/2y. Once we have our rearranged formula, we can find the reciprocal of b, which is 1/b. Therefore, 1/b = 2y/(y-2x).

Finally, to find our desired expression, the expression of 2/b in terms of x and y, we multiply our expression of 1/b by 2, resulting in: 2/b = 4y/(y-2x).

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Answers

Of course it can. It always is if 'x' is less than 2.

Yes, it can.

See inequality:

x-2 < 0
x < 2

So, any value of x smaller than 2 become x- 2 a negative result.

True or False: 1. all trapezoids are scalene? 2. all squares are rhombuses? 3. all rectangles are squares? 4. all squares are rectangles? 5. all parallelograms are squares?

Answers

false, because are not the same thing because a square Is not a triangle so these aren't trapezoids at all because all trapezoids are not scalence

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