Quadratic Equations
Nature of roots
Grade 11
Question:
<p>If <\(ax^2 + bx + c = 0\), \(a, b, c \in R\) has no real roots, and if \(c < 0\), then which of the following is true?</p>
<p>(a) \(a < 0\)</p>
<p>(b) \(a + b + c > 0\)</p>
<p>(c) \(a > 0\)</p>
Step-by-Step Solution
Key Concept: The question appears incomplete, but typically for quadratic equations, the key insight involves recognizing the relationship between roots and coefficients (Vieta's formulas) or the discriminant condition that determines the nature of roots.
<p><strong>Note:</strong> The question statement is incomplete. Please provide the full question.</p><p>For a quadratic equation ax² + bx + c = 0:</p><p><strong>Vieta's Formulas:</strong></p><ul><li>Sum of roots: α + β = -b/a</li><li>Product of roots: αβ = c/a</li></ul><p><strong>Discriminant:</strong> Δ = b² - 4ac</p><ul><li>If Δ > 0: Two distinct real roots</li><li>If Δ = 0: Equal roots</li><li>If Δ < 0: Complex conjugate roots</li></ul><p>∴ Answer: Cannot be determined without complete question</p>
Correct Answer: a