Select all correct answers.
One solution to a quadratic equation is . Which sentences could describe any remaining solutions?
There are at least two more real solutions.
There are no other real solutions because of repeated roots.
There are no complex solutions.
There is exactly one complex solution.
There is exactly one more real solution.
There are two or more complex solutions.

Question

Select all correct answers.
One solution to a quadratic equation is

. Which sentences could describe any remaining solutions?
There are at least two more real solutions.
There are no other real solutions because of repeated roots.
There are no complex solutions.
There is exactly one complex solution.
There is exactly one more real solution.
There are two or more complex solutions.

UpStudy AI · Accepted Answer

We know that a quadratic equation can have at most two solutions. Given that one solution is $$ x = -\frac{5}{3} $$, we need to analyze the possible remaining solutions.
Let's evaluate each statement based on the properties of quadratic equations:1. **There are at least two more real solutions.**  
   - **Incorrect.** A quadratic equation can have at most two solutions, and we already have one.

2. **There are no other real solutions because of repeated roots.**  
   - **Possible.** If the quadratic has a repeated root, then the other solution would also be $$ x = -\frac{5}{3} $$.

3. **There are no complex solutions.**  
   - **Incorrect.** If there is one real solution, there could still be complex solutions depending on the discriminant.

4. **There is exactly one complex solution.**  
   - **Incorrect.** A quadratic equation cannot have only one complex solution; complex solutions come in conjugate pairs.

5. **There is exactly one more real solution.**  
   - **Possible.** If the quadratic has two distinct real solutions, then there would be exactly one more real solution.

6. **There are two or more complex solutions.**  
   - **Incorrect.** A quadratic equation can have at most two solutions, and if one is real, the other must be either real or complex (but not more than two total).
The correct sentences that could describe any remaining solutions are: - There are no other real solutions because of repeated roots. - There is exactly one more real solution.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Algebra Questions