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Answer :
To solve the equation [tex]\(15x^2 + 13x = 0\)[/tex] using the quadratic formula, we need to first understand the standard form of a quadratic equation, which is [tex]\(ax^2 + bx + c = 0\)[/tex]. In this case, [tex]\(a = 15\)[/tex], [tex]\(b = 13\)[/tex], and [tex]\(c = 0\)[/tex].
However, since there's no constant term (c=0), we can actually solve this by factoring instead. The equation can be rewritten as:
[tex]\[ x(15x + 13) = 0 \][/tex]
This shows that the product of two factors is zero. According to the zero product property, at least one of the factors must be zero for the product to be zero. Therefore, we set each factor equal to zero:
1. [tex]\( x = 0 \)[/tex]
2. [tex]\( 15x + 13 = 0 \)[/tex]
Let's solve the second equation:
For [tex]\( 15x + 13 = 0 \)[/tex]:
- Subtract 13 from both sides:
[tex]\( 15x = -13 \)[/tex]
- Divide both sides by 15:
[tex]\( x = -\frac{13}{15} \)[/tex]
Therefore, the solutions to the equation [tex]\( 15x^2 + 13x = 0 \)[/tex] are:
[tex]\( x = 0 \)[/tex] and [tex]\( x = -\frac{13}{15} \)[/tex]
The correct answer from the given choices is:
a. [tex]\( x = -\frac{13}{15}, 0 \)[/tex]
However, since there's no constant term (c=0), we can actually solve this by factoring instead. The equation can be rewritten as:
[tex]\[ x(15x + 13) = 0 \][/tex]
This shows that the product of two factors is zero. According to the zero product property, at least one of the factors must be zero for the product to be zero. Therefore, we set each factor equal to zero:
1. [tex]\( x = 0 \)[/tex]
2. [tex]\( 15x + 13 = 0 \)[/tex]
Let's solve the second equation:
For [tex]\( 15x + 13 = 0 \)[/tex]:
- Subtract 13 from both sides:
[tex]\( 15x = -13 \)[/tex]
- Divide both sides by 15:
[tex]\( x = -\frac{13}{15} \)[/tex]
Therefore, the solutions to the equation [tex]\( 15x^2 + 13x = 0 \)[/tex] are:
[tex]\( x = 0 \)[/tex] and [tex]\( x = -\frac{13}{15} \)[/tex]
The correct answer from the given choices is:
a. [tex]\( x = -\frac{13}{15}, 0 \)[/tex]
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