Answer :
To solve the equation [tex]\(15x^2 + 13x = 0\)[/tex] using the quadratic formula, let's first identify the coefficients of the quadratic equation. The standard form of a quadratic equation is [tex]\(ax^2 + bx + c = 0\)[/tex]. In this case:
- [tex]\(a = 15\)[/tex]
- [tex]\(b = 13\)[/tex]
- [tex]\(c = 0\)[/tex]
The quadratic formula is:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
Let's calculate the solutions step-by-step:
1. Find the discriminant:
[tex]\[
b^2 - 4ac = 13^2 - 4 \times 15 \times 0 = 169
\][/tex]
2. Calculate the square root of the discriminant:
[tex]\[
\sqrt{169} = 13
\][/tex]
3. Plug values into the quadratic formula:
- The first solution is:
[tex]\[
x_1 = \frac{-b + \sqrt{b^2 - 4ac}}{2a} = \frac{-13 + 13}{30} = \frac{0}{30} = 0
\][/tex]
- The second solution is:
[tex]\[
x_2 = \frac{-b - \sqrt{b^2 - 4ac}}{2a} = \frac{-13 - 13}{30} = \frac{-26}{30} = -\frac{13}{15}
\][/tex]
The solutions to the equation [tex]\(15x^2 + 13x = 0\)[/tex] are [tex]\(x = 0\)[/tex] and [tex]\(x = -\frac{13}{15}\)[/tex].
Therefore, the correct choice is:
- A. [tex]\(x = -\frac{13}{15}, 0\)[/tex]
- [tex]\(a = 15\)[/tex]
- [tex]\(b = 13\)[/tex]
- [tex]\(c = 0\)[/tex]
The quadratic formula is:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
Let's calculate the solutions step-by-step:
1. Find the discriminant:
[tex]\[
b^2 - 4ac = 13^2 - 4 \times 15 \times 0 = 169
\][/tex]
2. Calculate the square root of the discriminant:
[tex]\[
\sqrt{169} = 13
\][/tex]
3. Plug values into the quadratic formula:
- The first solution is:
[tex]\[
x_1 = \frac{-b + \sqrt{b^2 - 4ac}}{2a} = \frac{-13 + 13}{30} = \frac{0}{30} = 0
\][/tex]
- The second solution is:
[tex]\[
x_2 = \frac{-b - \sqrt{b^2 - 4ac}}{2a} = \frac{-13 - 13}{30} = \frac{-26}{30} = -\frac{13}{15}
\][/tex]
The solutions to the equation [tex]\(15x^2 + 13x = 0\)[/tex] are [tex]\(x = 0\)[/tex] and [tex]\(x = -\frac{13}{15}\)[/tex].
Therefore, the correct choice is:
- A. [tex]\(x = -\frac{13}{15}, 0\)[/tex]
