Question

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

Answer 1

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Answer 2

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.