Which of the following is a zero for the function f(x) = (x + 3)(x − 7)(x + 5)? x = −7 x = −3 x =

Question

Which of the following is a zero for the function f(x) = (x + 3)(x − 7)(x + 5)?

x = −7

x = −3

x = 3

x = 5

0

Answers ( No )

    0
    2021-09-20T23:32:34+00:00

    ANSWER

    The zero of
    f(x) = (x + 3)(x - 7)(x + 5)

    among the given options is

    x =  - 3

    EXPLANATION

    The given function is
    f(x) = (x + 3)(x - 7)(x + 5)

    To find the zeros of the given function, we set

    f(x) = 0

    This implies that,

    (x + 3)(x - 7)(x + 5) = 0

    Either

    (x + 3) = 0 \: or \: (x - 7) = 0 \: or(x + 5) = 0

    This gives us,

    x =  - 3 \: or \: x = 7 \: or \: x  =  - 5

    From the options provided, the only zero is

    x =  - 3
    The correct answer is option B.

    0
    2021-09-20T23:33:03+00:00

    The zero of the function f\left( x \right)=\left( {x + 3} \right)\left({x - 7} \right)\left( {x + 5} \right) is \boxed{x =  - 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 given options are as follows,

    (a).x =  - 7

    (b).x =  - 3

    (c).x = 3

    (d).x = 5

    Explanation:

    The given function is f\left( x \right) = \left( {x + 3} \right)\left( {x - 7} \right)\left( {x + 5} \right).

    Solve the function to obtain the zeroes.

    \left( {x + 3} \right)\left( {x - 7} \right)\left( {x + 5} \right) = 0

    Either x+3=0 or x-7=0 or x+5=0.

    The first zero of the function can be obtained as follows,

    \begin{aligned}\left({x + 3} \right)&= 0\\x&= - 3\\\end{aligned}

    The second zero of the function can be obtained as follows,

    \begin{aligned}x - 7&= 0\\x&= 7\\\end{aligned}

    The third zero of the function can be calculated as follows,

    \begin{aligned}x + 5&= 0\\x&= - 5\\\end{aligned}

    The zeros of the functions are -3, 7 and -5.

    The zero of the function f\left( x \right)=\left( {x + 3}\right)\left( {x - 7}\right)\left( {x + 5}\right) is \boxed{x =  - 3}.

    Option (a) is not correc tx =  - 7 is not a root of the function.

    Option (b) is correct as x=-3 is the root of the function.

    Option (c) is not correct {\text{x}=3 is not a root of the function.

    Option (d) is not correct x = 5 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,f\left( x \right) = \left( {x + 3} \right)\left( {x - 7} \right)\left( {x + 5} \right), solution, cubic function, degree of the function.

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