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Gnesinka [82]
3 years ago
8

Which of the following is the complete list of roots for the polynomial function f(x)(x^2+2x-15)?–5, 3 –5, 3, –4 + i, –4 – i –5,

3, –4 + i, 4 + i –4 + i, –4 – i

Mathematics
2 answers:
Advocard [28]3 years ago
5 0
Hey there !

Check the attachment.
Hope it helps you :)

Valentin [98]3 years ago
5 0

The complete roots of the function f\left( x \right)=\left({{x^2} + 2x - 15}\right) are \boxed{ - 5{\text{ and 3}}}.

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.

Given:

The function is f\left( x \right)=\left({{x^2} + 2x - 15}\right).

Explanation:

To obtain the roots of the polynomial function substitute 0 for f\left( x \right)=\left( {{x^2} + 2x - 15}\right).

\begin{aligned}f\left( x \right)&= 0\\{x^2} + 2x - 15&= 0\\{x^2}+5x - 3x-15&= 0\\ x\left({x + 5} \right)- 3\left( {x + 5} \right)&= 0\\\left({x - 3}\right)\left({x + 5} \right)&= 0\\\end{aligned}

The complete roots of the function f\left( x \right)=\left({{x^2} + 2x - 15}\right) are \boxed{ - 5{\text{ and 3}}}.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear equation

Keywords: roots, linear equation, quadratic equation, zeros, function, polynomial, solution, cubic function, degree of the function.

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<h3>An equation in the form y = ...</h3>

The statement is given as:

'y is one less than a quarter of x'

A quarter of x means x/4

So, we have:

y = x/4 - 1

Hence, an equation in the form of y is y = x/4 - 1

<h3>Number sentences</h3>

From the question, we have:

x = -4, -2,0, 2 and 4

Substitute these values in y = x/4 - 1

-4/4 - 1 = -2

-2/4 - 1 = -1.5

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The above represents the number sentences

<h3>The flow diagram</h3>

This is represented as:

x                     Computation           y

-4                    -4/4 - 1                     -2

-2                    -2/4 - 1                     -1.5

-0                    -0/4 - 1                     -1

2                      2/4 - 1                     -0.5

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This is represented as:

x   y

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This is represented as:

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Step-by-step explanation:

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we can substitute the equation of T2 into T4 but we first need to rewrite T4

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