No Real Roots When D < 0
If the discriminant of a quadratic equation is negative, the equation has no real roots.
Practice This ConceptMain explanation
Teacher explanation
A negative discriminant means the square-root part in the quadratic formula cannot produce a real number. So the equation does not have real solutions.
Example
x^2 + 2x + 5 = 0 has D = 4 - 20 = -16, so it has no real roots.
Simple analogy
Negative D means no real answer.
Common confusion
Students sometimes try to find real answers even after getting a negative discriminant.
Exam tip
If D is negative, state clearly that the equation has no real roots and stop there unless complex roots are asked.
Answer writing and exam use
1-mark use
Write the exact meaning of no real roots when d < 0 in one clean line.
2-mark use
Define no real roots when d < 0 and add one example or condition.
3-mark use
Explain no real roots when d < 0, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
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