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Solve the equation using the quadratic formula:

[tex]15x^2 + 13x = 0[/tex]

a. [tex]x = -\frac{13}{15}, 0[/tex]
b. [tex]x = 0[/tex]
c. [tex]x = \frac{13}{15}, 0[/tex]
d. [tex]x = \pm \frac{13}{15}[/tex]

Please select the best answer from the choices provided:
A
B
C
D

Answer :

To solve the equation [tex]\(15x^2 + 13x = 0\)[/tex] using the quadratic formula, let's go through it step-by-step.

The quadratic formula is:

[tex]\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\][/tex]

For the equation [tex]\(15x^2 + 13x = 0\)[/tex], we can identify the coefficients as follows:
- [tex]\(a = 15\)[/tex]
- [tex]\(b = 13\)[/tex]
- [tex]\(c = 0\)[/tex]

Since it is a quadratic equation and [tex]\(c = 0\)[/tex], we can factor out an [tex]\(x\)[/tex] from the equation as well:

[tex]\[
x(15x + 13) = 0
\][/tex]

This gives us two potential solutions:

1. [tex]\(x = 0\)[/tex]
2. [tex]\(15x + 13 = 0\)[/tex]

Solving [tex]\(15x + 13 = 0\)[/tex]:

[tex]\[
15x = -13
\][/tex]
[tex]\[
x = -\frac{13}{15}
\][/tex]

Thus, we have the solutions:
- [tex]\(x = 0\)[/tex]
- [tex]\(x = -\frac{13}{15}\)[/tex]

Based on the choices provided:
- a. [tex]\(x = -\frac{13}{15}, 0\)[/tex]

So, the correct answer is A.

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