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Answer :
To solve the equation [tex]\(15x^2 + 13x = 0\)[/tex] using the quadratic formula, let's first review the quadratic formula, which is:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
In this equation, [tex]\(a = 15\)[/tex], [tex]\(b = 13\)[/tex], and [tex]\(c = 0\)[/tex].
1. Identify the coefficients:
- [tex]\(a = 15\)[/tex]
- [tex]\(b = 13\)[/tex]
- [tex]\(c = 0\)[/tex]
2. Calculate the discriminant:
The discriminant [tex]\(b^2 - 4ac\)[/tex] is part of the quadratic formula. We calculate it as follows:
[tex]\[
\text{Discriminant} = b^2 - 4ac = 13^2 - 4 \cdot 15 \cdot 0 = 169 - 0 = 169
\][/tex]
3. Calculate the roots using the quadratic formula:
- Since [tex]\(c = 0\)[/tex], the equation simplifies significantly, and we can set [tex]\(x(15x + 13) = 0\)[/tex]. This gives two potential solutions:
- [tex]\(x = 0\)[/tex]
- [tex]\(15x + 13 = 0\)[/tex], solve for [tex]\(x\)[/tex]:
[tex]\[
15x = -13 \\
x = -\frac{13}{15}
\][/tex]
4. Conclusion:
The solutions to the equation [tex]\(15x^2 + 13x = 0\)[/tex] are [tex]\(x = 0\)[/tex] and [tex]\(x = -\frac{13}{15}\)[/tex].
Comparing these solutions with the provided options:
- a. [tex]\(x = -\frac{13}{15}, 0\)[/tex] is correct.
Therefore, the best answer is A.
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
In this equation, [tex]\(a = 15\)[/tex], [tex]\(b = 13\)[/tex], and [tex]\(c = 0\)[/tex].
1. Identify the coefficients:
- [tex]\(a = 15\)[/tex]
- [tex]\(b = 13\)[/tex]
- [tex]\(c = 0\)[/tex]
2. Calculate the discriminant:
The discriminant [tex]\(b^2 - 4ac\)[/tex] is part of the quadratic formula. We calculate it as follows:
[tex]\[
\text{Discriminant} = b^2 - 4ac = 13^2 - 4 \cdot 15 \cdot 0 = 169 - 0 = 169
\][/tex]
3. Calculate the roots using the quadratic formula:
- Since [tex]\(c = 0\)[/tex], the equation simplifies significantly, and we can set [tex]\(x(15x + 13) = 0\)[/tex]. This gives two potential solutions:
- [tex]\(x = 0\)[/tex]
- [tex]\(15x + 13 = 0\)[/tex], solve for [tex]\(x\)[/tex]:
[tex]\[
15x = -13 \\
x = -\frac{13}{15}
\][/tex]
4. Conclusion:
The solutions to the equation [tex]\(15x^2 + 13x = 0\)[/tex] are [tex]\(x = 0\)[/tex] and [tex]\(x = -\frac{13}{15}\)[/tex].
Comparing these solutions with the provided options:
- a. [tex]\(x = -\frac{13}{15}, 0\)[/tex] is correct.
Therefore, the best answer is A.
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