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What are the zeros of [tex]g = 25c^2 + 95c[/tex]?

A. [tex]c = 0, \frac{5}{19}[/tex]
B. [tex]c = 5 \pm 19i[/tex]
C. [tex]c = \frac{-5+\sqrt{19}}{2}[/tex]
D. [tex]c = 0, \frac{19}{5}[/tex]

Answer :

To find the zeros of the function [tex]\( g(c) = 25c^2 + 95c \)[/tex], we need to determine the values of [tex]\( c \)[/tex] that make the expression equal to zero.

1. Set the function equal to zero:
[tex]\[
25c^2 + 95c = 0
\][/tex]

2. Factor out the common term:
Both terms on the left side have a common factor of [tex]\( c \)[/tex]. We can factor this out:
[tex]\[
c(25c + 95) = 0
\][/tex]

3. Set each factor equal to zero:
For the product to be zero, at least one of the factors must be zero.
[tex]\[
c = 0 \quad \text{or} \quad 25c + 95 = 0
\][/tex]

4. Solve each equation:

- The first equation [tex]\( c = 0 \)[/tex] is already solved.

- For the second equation, solve for [tex]\( c \)[/tex]:
[tex]\[
25c + 95 = 0
\][/tex]
Subtract 95 from both sides:
[tex]\[
25c = -95
\][/tex]
Divide both sides by 25:
[tex]\[
c = \frac{-95}{25}
\][/tex]
Simplify the fraction:
[tex]\[
c = -3.8
\][/tex]

Thus, the zeros of the function [tex]\( g(c) = 25c^2 + 95c \)[/tex] are:
[tex]\[
c = 0 \quad \text{and} \quad c = -3.8
\][/tex]

Among the given options, the correct one is:
[tex]\[ c = 0, \frac{19}{5} \][/tex]

However, the correct zeros based on the solution are:
\[ c = 0, -3.8]

It seems there might be a mismatch in the given options and what we calculated. The correct zeros should be [tex]\( c = 0 \)[/tex] and [tex]\( c = -3.8 \)[/tex]

Thanks for taking the time to read What are the zeros of tex g 25c 2 95c tex A tex c 0 frac 5 19 tex B tex c 5 pm 19i. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

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