Find the discriminant of the quadratic equation $4x^2 - 5 = 0$ and hence comment on the nature of roots of the equation.
Generated by claude-sonnet-4-6 · 2026-06-15 10:30 · grounding rag
Model Answer
For $4x^2 - 5 = 0$, we have $a = 4$, $b = 0$, $c = -5$.
Discriminant $= b^2 - 4ac = (0)^2 - 4(4)(-5) = 0 + 80 = 80$
Since $D = 80 > 0$, the equation has two distinct real roots.
Source: Chapter 4, Section 4.4 – Nature of Roots
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Explanation
- Identify $a$, $b$, $c$ correctly — here $b = 0$ since there is no $x$ term.
- The discriminant formula is $D = b^2 - 4ac$; examiners want you to substitute values clearly.
- State the conclusion using standard language: "two distinct real roots" (D > 0), "two equal real roots" (D = 0), or "no real roots" (D < 0).
- Both the calculation and the nature comment carry marks, so don't skip either step.