Answer:
The equation 0 = 3x² + 17x - 160 might be useful in determining the length.
Step-by-step explanation:
The area of the vegetable garden is specified as 170 ft².
Now, regarding the provided equations;
1) For 0 = 3x² + 2x + 180, applying the quadratic formula results in:
x = [-2 ± √(3² - 4(3 × 180)]/(2 × 3)
x = [-2 ± √(-2151)]/6
The square root value is negative, indicating no real solution for x.
Thus, this equation does not help find the length.
2) For the equation 0 = 3x² + 10x + 180, employing the quadratic formula, the square root value is also negative, hence there's no natural root for x. This means this equation can't be used to determine the length.
3) For 0 = 3x² + 17x - 160, the roots when using the quadratic formula yield -10.67 or 5. The value 5 is viable since it is a whole number. Considering the area is also a whole number, this equation can be applied to ascertain the length.
4) For 0 = 3x² - 160, simplifying gives;
3x² = 160
x² = 160/3
x = ±√(160/3)
x = ±7.303
Since the area is a whole number but this length isn't, this equation may not accurately determine the length.
