Discriminant
The discriminant of a quadratic equation ax^2 + bx + c = 0 is D = b^2 - 4ac.
Practice This ConceptMain explanation
Teacher explanation
The discriminant tells us about the roots before we actually solve the equation. By checking D, we can see whether the roots are real, equal, or not real.
Example
For x^2 - 4x + 1 = 0, D = (-4)^2 - 4(1)(1) = 12.
Simple analogy
Discriminant decides the kind of roots.
Common confusion
Students often forget that b includes its sign and write b^2 with the wrong value.
Exam tip
Use the discriminant first when the question asks about the nature of roots.
Answer writing and exam use
1-mark use
Write the exact meaning of discriminant in one clean line.
2-mark use
Define discriminant and add one example or condition.
3-mark use
Explain discriminant, show the method or example, and mention the common mistake.
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