Question

Which of the equations has one solution that is 5/4 Select all that apply.

(3 points)

4x ^ 2 - x = 5

4x ^ 2 + 3x = - 10

4x ^ 2 - 13x + 10 = 0

4x ^ 2 + x + 5 = 0

4x ^ 2 + 3x - 10 = 0

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find out which equation has a solution of 5/4, we need to solve each equation and see if 5/4 is one of the solutions.

1. 4x^2 - x = 5:
Rearranging the equation, we get 4x^2 - x - 5 = 0.
Solving this quadratic equation, we find x ≈ -1.25 or x ≈ 1.25.
Therefore, this equation does not have a solution of 5/4.

2. 4x^2 + 3x = -10:
Rearranging the equation, we get 4x^2 + 3x + 10 = 0.
Solving this quadratic equation, we find no real solutions.
Therefore, this equation does not have a solution of 5/4.

3. 4x^2 - 13x + 10 = 0:
Using factoring or the quadratic formula, we find the solutions to be x = 2.5 or x = 2.
Therefore, this equation does not have a solution of 5/4.

4. 4x^2 + x + 5 = 0:
Using the quadratic formula, we find the solutions to be x ≈ -1.05 + 0.99i and x ≈ -1.05 - 0.99i.
Therefore, this equation does not have a solution of 5/4.

5. 4x^2 + 3x - 10 = 0:
Using factoring or the quadratic formula, we find the solutions to be x = -2 and x = 1.25.
Therefore, this equation has a solution of 5/4.

Therefore, the only equation that has a solution of 5/4 is 4x^2 + 3x - 10 = 0.