Solve the factored quadratic equation (13x+3)(9x−14)=0

Question

.(1 point)
Responses

A) The solution set is x={−13/3,9/14}
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The solution set is x equals left brace negative Start Fraction 13 over 3 End Fraction comma Start Fraction 9 over 14 End Fraction right brace .

B) The solution set is x={−3/13,9/14}
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The solution set is x equals left brace negative Start Fraction 3 over 13 End Fraction comma Start Fraction 9 over 14 End Fraction right brace .

C) The solution set is x={−3,14}
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The solution set is x equals left brace negative 3 comma 14 right brace .

D) The solution set is x={−3/13,1 5/9}
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The solution set is x equals left brace negative Start Fraction 3 over 13 End Fraction comma 1 Start Fraction 5 over 9 End Fraction right brace .

Answer 1

To solve the factored quadratic equation \((13x + 3)(9x - 14) = 0\), we can set each factor equal to zero and solve for \(x\).

1. Set the first factor to zero: \[ 13x + 3 = 0 \] \[ 13x = -3 \] \[ x = -\frac{3}{13} \]

2. Set the second factor to zero: \[ 9x - 14 = 0 \] \[ 9x = 14 \] \[ x = \frac{14}{9} \]

Now we have two solutions:

• \(x = -\frac{3}{13}\)
• \(x = \frac{14}{9}\)

Thus, the solution set is: \[ x = \left{ -\frac{3}{13}, \frac{14}{9} \right} \]

Looking at the answer choices provided, none of them match directly, but it seems that "1 5/9" could mean "14/9" represented incorrectly.

If we consider "1 5/9" as equivalent to \(14/9\):

The closest response given the context is: D) The solution set is \( x = \left{ -\frac{3}{13}, 1 \frac{5}{9} \right} \).

So, option D is the correct choice.