Respuesta :
ANSWER
The zero of
[tex]f(x) = (x + 3)(x - 7)(x + 5)[/tex]
among the given options is
[tex]x = - 3[/tex]
EXPLANATION
The given function is
[tex]f(x) = (x + 3)(x - 7)(x + 5)[/tex]
To find the zeros of the given function, we set
[tex]f(x) = 0[/tex]
This implies that,
[tex](x + 3)(x - 7)(x + 5) = 0[/tex]
Either
[tex](x + 3) = 0 \: or \: (x - 7) = 0 \: or(x + 5) = 0[/tex]
This gives us,
[tex]x = - 3 \: or \: x = 7 \: or \: x = - 5[/tex]
From the options provided, the only zero is
[tex]x = - 3[/tex]
The correct answer is option B.
The zero of
[tex]f(x) = (x + 3)(x - 7)(x + 5)[/tex]
among the given options is
[tex]x = - 3[/tex]
EXPLANATION
The given function is
[tex]f(x) = (x + 3)(x - 7)(x + 5)[/tex]
To find the zeros of the given function, we set
[tex]f(x) = 0[/tex]
This implies that,
[tex](x + 3)(x - 7)(x + 5) = 0[/tex]
Either
[tex](x + 3) = 0 \: or \: (x - 7) = 0 \: or(x + 5) = 0[/tex]
This gives us,
[tex]x = - 3 \: or \: x = 7 \: or \: x = - 5[/tex]
From the options provided, the only zero is
[tex]x = - 3[/tex]
The correct answer is option B.
The zero of the function [tex]f\left( x \right)=\left( {x + 3} \right)\left({x - 7} \right)\left( {x + 5} \right)[/tex] is [tex]\boxed{x = - 3}.[/tex]
Further explanation:
The Fundamental Theorem of Algebra states that the polynomial has n roots if the degree of the polynomial is n.
[tex]f\left( x \right)= a{x^n} + b{x^{n - 1}}+ \ldots + cx + d[/tex]
The polynomial function has n roots or zeroes.
Given:
The given options are as follows,
(a).[tex]x = - 7[/tex]
(b).[tex]x = - 3[/tex]
(c).[tex]x = 3[/tex]
(d).[tex]x = 5[/tex]
Explanation:
The given function is [tex]f\left( x \right) = \left( {x + 3} \right)\left( {x - 7} \right)\left( {x + 5} \right).[/tex]
Solve the function to obtain the zeroes.
[tex]\left( {x + 3} \right)\left( {x - 7} \right)\left( {x + 5} \right) = 0[/tex]
Either [tex]x+3=0[/tex] or [tex]x-7=0[/tex] or [tex]x+5=0.[/tex]
The first zero of the function can be obtained as follows,
[tex]\begin{aligned}\left({x + 3} \right)&= 0\\x&= - 3\\\end{aligned}[/tex]
The second zero of the function can be obtained as follows,
[tex]\begin{aligned}x - 7&= 0\\x&= 7\\\end{aligned}[/tex]
The third zero of the function can be calculated as follows,
[tex]\begin{aligned}x + 5&= 0\\x&= - 5\\\end{aligned}[/tex]
The zeros of the functions are -3, 7 and -5.
The zero of the function [tex]f\left( x \right)=\left( {x + 3}\right)\left( {x - 7}\right)\left( {x + 5}\right)[/tex] is [tex]\boxed{x = - 3}.[/tex]
Option (a) is not correc [tex]tx = - 7[/tex] is not a root of the function.
Option (b) is correct as [tex]x=-3[/tex] is the root of the function.
Option (c) is not correct [tex]{\text{x}=3[/tex] is not a root of the function.
Option (d) is not correct [tex]x = 5[/tex] is not a root of the function
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: Linear equation, quadratic equation, zeros, function,[tex]f\left( x \right) = \left( {x + 3} \right)\left( {x - 7} \right)\left( {x + 5} \right),[/tex] solution, cubic function, degree of the function.
