Mathematics, 09.10.2019 22:00 bwelsh880

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

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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 from: leonardoocampo7555

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 $\boxed7.$

Learn more:

1. Learn more about inverse of the functionhttps://.

2. Learn more about equation of circle .

3. Learn more about range and domain of the function

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.

Answer from: Quest

an advantage of the standard deviation is that it increases as the dispersion of the data increases. e. the interquartile range is preferred when the data are not skewed or no have outliers. an advantage of the standard deviation is that it uses all the observations in its computation.

Answer from: Quest

solution:

the given function is ,

$f(x) = 4 x^3 - 72 x^2 + 320 x,$

= $4x( x^2- 18 x + 80)\\\\ 4 x(x^2-10 x -8 x + 80) \\\\ 4 x[(x-10)(x-8)]$

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

$f(x) = a x^3+ b x^2 + c x+d,$

sum of the roots = a + b +c= 0+8+10=18= $\frac{-b}{a}$

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 = $\frac{c}{a}$

product of roots = a b c = 0= $\frac{d}{a}$

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function $f(x) = 4 x^3 - 72 x^2 + 320 x,$ is given by entry and exit route of this hall.

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