Nature of Roots Based on Discriminant
The nature of roots depends on the discriminant D: if D > 0 the roots are real and distinct, if D = 0 they are real and equal, and if D < 0 they are not real.
Practice This ConceptMain explanation
Teacher explanation
This rule saves time in exams because the nature of roots can be predicted without solving the whole equation. It is one of the fastest checks in quadratic equations.
Example
If D = 25, the roots are real and distinct; if D = 0, the roots are equal; if D = -9, there are no real roots.
Simple analogy
Positive, zero, negative: distinct, equal, none.
Common confusion
Students sometimes say any positive D gives equal roots, which is incorrect.
Exam tip
Memorise the sign rule carefully: positive means distinct, zero means equal, negative means no real roots.
Answer writing and exam use
1-mark use
Write the exact meaning of nature of roots based on discriminant in one clean line.
2-mark use
Define nature of roots based on discriminant and add one example or condition.
3-mark use
Explain nature of roots based on discriminant, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
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