Part 2: Use the discriminant to determine the number of real solutions the equation has.(1 point) Responses 2 complex solutions 2 complex solutions 1 real solution, multiplicity 2 1 real solution, multiplicity 2

Answer 1

To determine the number of real solutions to a quadratic equation, we can use the discriminant, which is given by the formula:

$$D=b^2-4ac$$

where $a$, $b$, and $c$ are the coefficients of the quadratic equation in the form $a{x}^2+bx+c=0$.

The interpretation of the discriminant is as follows:

• If $D>0$: There are 2 distinct real solutions.
• If $D=0$: There is 1 real solution (with multiplicity 2).
• If $D<0$: There are 2 complex (non-real) solutions.

Given your responses:

• 2 complex solutions
• 1 real solution, multiplicity 2

If you provide a specific quadratic equation, I can help you calculate the discriminant and determine the number of real solutions based on the values of $a$, $b$, and $c$.