Basic Mathematics for Pharmacy
MathematicsLesson 1 of 3
Quadratic Equations, Parabolas & Factoring
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Quadratic algebra forms the backbone of quantitative problems in science entrance exams.
Quadratic Formula: x=\frac{−b \pm \sqrt{b2−4ac}}{2a}
- Discriminant \Delta = b^2 - 4ac:
- \Delta > 0 \implies 2 distinct real roots.
- \Delta = 0 \implies 2 equal real roots (x = -b / 2a).
- \Delta < 0 \implies no real roots.
- Vieta's Formulas: Sum of roots x_1 + x_2 = -\frac{b}{a}, Product of roots x_1 \cdot x_2 = \frac{c}{a}.
- Parabola Vertex: V = \left(-\frac{b}{2a}, -\frac{\Delta}{4a}\right).
- Calculate discriminant Delta to check root existence.
- Solve using quadratic formula or factoring.
- Determine parabola concavity based on the sign of a.
Exam strategy
Focus on understanding underlying concepts — exam questions test application, not memorization.
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