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How many real solutions can a quadratic equation have?
3 Answers
- ?Lv 74 years ago
A quadratic MUST have 2 solutions per the Fundamental Theorem of Algebra.
However, that can be a combination of 0-2 Real solutions, with the remaining solutions being Imaginary.
Since the degree of a Quadratic is 2, up to 2 real solutions.
For degree of 3, then up to 3 solutions, etc., etc.
Here's 3 examples:
x² – 2x – 3 = 0
two distinct real-number solutions
x² – 6x + 9 = 0
one (repeated) real-number solution
x² + 3x + 3 = 0
no real-number solutions, 2 imaginary solutions
