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 \(ax^2 + bx + c = 0\).
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 \(c\).
1 answer