The complete roots of the function [tex]f\left( x \right)=\left({{x^2} + 2x - 15}\right)[/tex] are [tex]\boxed{ - 5{\text{ and 3}}}.[/tex]
Further explanation:
The Fundamental Theorem of Algebra states that the polynomial has n roots if the degree of the polynomial is [tex]n.[/tex]
[tex]f\left( x \right) = a{x^n} + b{x^{n - 1}} + \ldots + cx + d[/tex]
The polynomial function has [tex]n[/tex] roots or zeroes.
Given:
The function is [tex]f\left( x \right)=\left({{x^2} + 2x - 15}\right).[/tex]
Explanation:
To obtain the roots of the polynomial function substitute [tex]0[/tex] for [tex]f\left( x \right)=\left( {{x^2} + 2x - 15}\right).[/tex]
[tex]\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}[/tex]
The complete roots of the function [tex]f\left( x \right)=\left({{x^2} + 2x - 15}\right)[/tex] are [tex]\boxed{ - 5{\text{ and 3}}}.[/tex]
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 https://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.
