which of the following equations has the solution set x = {-9/5, 3}

Answer 1

To determine which equation has the solution set \( x = \left{-\frac{9}{5}, 3\right} \), we can create a polynomial that has these roots. If \( x = -\frac{9}{5} \) and \( x = 3 \) are the roots, then we can use the factored form of a polynomial.

1. The factors corresponding to the roots will be:

   • For \( x = -\frac{9}{5} \): \( x + \frac{9}{5} \)
   • For \( x = 3 \): \( x - 3 \)

2. We can express the polynomial as: \[ P(x) = (x + \frac{9}{5})(x - 3) \]

3. To eliminate the fraction, we can multiply the entire equation by 5: \[ 5P(x) = 5\left(x + \frac{9}{5}\right)(x - 3) = (5x + 9)(x - 3) \]

4. Now, let's expand this: \[ = 5x^2 - 15x + 9x - 27 \] \[ = 5x^2 - 6x - 27 \]

Thus, the polynomial equation \( 5x^2 - 6x - 27 = 0 \) has the solution set \( x = \left{-\frac{9}{5}, 3\right} \).

If you have specific equations listed, please provide them, and we can determine which one matches this polynomial.

Answer 2

the specific equations
a. (x - 3) (9x + 5) = 0
b. -3x (5x + 9) = 0
c. (x - 3) (5x + 9) = 0
d. (x + 3) (9x - 5) = 0

Answer 3

To find out which equation has the solution set \( x = \left{-\frac{9}{5}, 3\right} \), we'll solve each of the given equations:

a. \( (x - 3)(9x + 5) = 0 \)

• Setting each factor to zero:
  • \( x - 3 = 0 \) gives \( x = 3 \)
  • \( 9x + 5 = 0 \) gives \( 9x = -5 \) or \( x = -\frac{5}{9} \)

Solution set: \( {3, -\frac{5}{9}} \)

b. \( -3x(5x + 9) = 0 \)

• Setting each factor to zero:
  • \( -3x = 0 \) gives \( x = 0 \)
  • \( 5x + 9 = 0 \) gives \( 5x = -9 \) or \( x = -\frac{9}{5} \)

Solution set: \( {0, -\frac{9}{5}} \)

c. \( (x - 3)(5x + 9) = 0 \)

• Setting each factor to zero:
  • \( x - 3 = 0 \) gives \( x = 3 \)
  • \( 5x + 9 = 0 \) gives \( 5x = -9 \) or \( x = -\frac{9}{5} \)

Solution set: \( {3, -\frac{9}{5}} \)

d. \( (x + 3)(9x - 5) = 0 \)

• Setting each factor to zero:
  • \( x + 3 = 0 \) gives \( x = -3 \)
  • \( 9x - 5 = 0 \) gives \( 9x = 5 \) or \( x = \frac{5}{9} \)

Solution set: \( {-3, \frac{5}{9}} \)

Summary of Solution Sets:

• a. \( {3, -\frac{5}{9}} \)
• b. \( {0, -\frac{9}{5}} \)
• c. \( {3, -\frac{9}{5}} \)
• d. \( {-3, \frac{5}{9}} \)

The equations that yield the solution set \( x = \left{-\frac{9}{5}, 3\right} \) is:

c. \( (x - 3)(5x + 9) = 0 \).