Answer :
To solve the equation [tex]\(15x^2 + 13x = 0\)[/tex] using the quadratic formula, let's go through the steps together.
The general form of a quadratic equation is [tex]\(ax^2 + bx + c = 0\)[/tex]. In this problem, the coefficients are:
- [tex]\(a = 15\)[/tex]
- [tex]\(b = 13\)[/tex]
- [tex]\(c = 0\)[/tex]
The quadratic formula to find the solutions of the equation is:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
### Step 1: Calculate the Discriminant
The discriminant is given by [tex]\(b^2 - 4ac\)[/tex].
[tex]\[
b^2 = 13^2 = 169
\][/tex]
[tex]\[
4ac = 4 \times 15 \times 0 = 0
\][/tex]
[tex]\[
\text{Discriminant} = 169 - 0 = 169
\][/tex]
### Step 2: Calculate the Roots
The roots are calculated using the quadratic formula:
For the positive root:
[tex]\[
x_1 = \frac{-b + \sqrt{169}}{2a} = \frac{-13 + 13}{30} = \frac{0}{30} = 0
\][/tex]
For the negative root:
[tex]\[
x_2 = \frac{-b - \sqrt{169}}{2a} = \frac{-13 - 13}{30} = \frac{-26}{30} = -\frac{13}{15}
\][/tex]
### Conclusion
The solutions to the equation are [tex]\(x = 0\)[/tex] and [tex]\(x = -\frac{13}{15}\)[/tex].
So, the best answer choice is:
C. [tex]\(x = \frac{13}{15}, 0\)[/tex]
(Note that [tex]\(15x^2 + 13x = 0\)[/tex] means the possible choice should be reconsidered as the individual parts were misprinted.)
However, considering the results obtained, these solutions match options (B. [tex]\(x = 0\)[/tex]) and (C. [tex]\(x = \frac{-13}{15}, 0\)[/tex]). But clearly, it should be:
C. [tex]\(x = -\frac{13}{15}, 0\)[/tex]
The general form of a quadratic equation is [tex]\(ax^2 + bx + c = 0\)[/tex]. In this problem, the coefficients are:
- [tex]\(a = 15\)[/tex]
- [tex]\(b = 13\)[/tex]
- [tex]\(c = 0\)[/tex]
The quadratic formula to find the solutions of the equation is:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
### Step 1: Calculate the Discriminant
The discriminant is given by [tex]\(b^2 - 4ac\)[/tex].
[tex]\[
b^2 = 13^2 = 169
\][/tex]
[tex]\[
4ac = 4 \times 15 \times 0 = 0
\][/tex]
[tex]\[
\text{Discriminant} = 169 - 0 = 169
\][/tex]
### Step 2: Calculate the Roots
The roots are calculated using the quadratic formula:
For the positive root:
[tex]\[
x_1 = \frac{-b + \sqrt{169}}{2a} = \frac{-13 + 13}{30} = \frac{0}{30} = 0
\][/tex]
For the negative root:
[tex]\[
x_2 = \frac{-b - \sqrt{169}}{2a} = \frac{-13 - 13}{30} = \frac{-26}{30} = -\frac{13}{15}
\][/tex]
### Conclusion
The solutions to the equation are [tex]\(x = 0\)[/tex] and [tex]\(x = -\frac{13}{15}\)[/tex].
So, the best answer choice is:
C. [tex]\(x = \frac{13}{15}, 0\)[/tex]
(Note that [tex]\(15x^2 + 13x = 0\)[/tex] means the possible choice should be reconsidered as the individual parts were misprinted.)
However, considering the results obtained, these solutions match options (B. [tex]\(x = 0\)[/tex]) and (C. [tex]\(x = \frac{-13}{15}, 0\)[/tex]). But clearly, it should be:
C. [tex]\(x = -\frac{13}{15}, 0\)[/tex]
