Answer :
To solve the equation [tex]\(15x^2 + 13x = 0\)[/tex] using the quadratic formula, we first need to identify the coefficients. The equation is in the form [tex]\(ax^2 + bx + c = 0\)[/tex], where:
- [tex]\(a = 15\)[/tex]
- [tex]\(b = 13\)[/tex]
- [tex]\(c = 0\)[/tex]
Since the constant term [tex]\(c\)[/tex] is 0, it's important to note that we can factor out an [tex]\(x\)[/tex] from the equation:
[tex]\[ 15x^2 + 13x = x(15x + 13) = 0 \][/tex]
Setting each factor equal to zero gives us two potential solutions:
1. [tex]\(x = 0\)[/tex]
2. [tex]\(15x + 13 = 0\)[/tex]
To solve the second equation, [tex]\(15x + 13 = 0\)[/tex], we can isolate [tex]\(x\)[/tex]:
[tex]\[ 15x = -13 \][/tex]
[tex]\[ x = -\frac{13}{15} \][/tex]
So, the solutions to the equation [tex]\(15x^2 + 13x = 0\)[/tex] are:
[tex]\[ x = 0 \quad \text{and} \quad x = -\frac{13}{15} \][/tex]
Thus, the correct answer from the given choices is:
a. [tex]\(x = -\frac{13}{15}, 0\)[/tex]
- [tex]\(a = 15\)[/tex]
- [tex]\(b = 13\)[/tex]
- [tex]\(c = 0\)[/tex]
Since the constant term [tex]\(c\)[/tex] is 0, it's important to note that we can factor out an [tex]\(x\)[/tex] from the equation:
[tex]\[ 15x^2 + 13x = x(15x + 13) = 0 \][/tex]
Setting each factor equal to zero gives us two potential solutions:
1. [tex]\(x = 0\)[/tex]
2. [tex]\(15x + 13 = 0\)[/tex]
To solve the second equation, [tex]\(15x + 13 = 0\)[/tex], we can isolate [tex]\(x\)[/tex]:
[tex]\[ 15x = -13 \][/tex]
[tex]\[ x = -\frac{13}{15} \][/tex]
So, the solutions to the equation [tex]\(15x^2 + 13x = 0\)[/tex] are:
[tex]\[ x = 0 \quad \text{and} \quad x = -\frac{13}{15} \][/tex]
Thus, the correct answer from the given choices is:
a. [tex]\(x = -\frac{13}{15}, 0\)[/tex]
