A quadratic equation is an equation of degree 2. The general form is:
Where:
are constants.
The solutions to this equation, often referred to as the roots or zeros of the equation, can be found using various methods.
Methods to Solve:
1. Factorization: If the quadratic can be factored, this method involves expressing the equation in the form are the roots.
2. Completing the Square: Convert the equation into a perfect square trinomial.
3. Quadratic Formula:
Application of Previous Concepts:
When we talk about the intersection of lines and curves:
- A quadratic equation can represent a parabola. If a line intersects this parabola, the point(s) of intersection can be found by solving the linear equation and the quadratic equation simultaneously.
Foundation Building Questions:
(Note: Again, I don't have access to specific previous year questions from management entrances post-2021, so I'll create a representative question based on the typical style of these exams.)
Question:
Solve for ( x) in the equation:
Solution:
Using the Quadratic Formula:
Where:
Plugging in the values:
So, the solutions are
Tips and Tricks:
1. Nature of Roots: Before solving, a quick check of the discriminant can give insight into the nature of the roots. If it's positive, there are two distinct roots; if zero, the roots are equal; if negative, the roots are imaginary.
2. Common Factors: Always look for common factors to simplify the equation before diving into solutions.
3. Graphical Insight: A quick sketch or mental visualisation of the parabola can give insights into the number and nature of the roots.
4. Intersection with Lines: If you need to find where a quadratic equation (parabola) intersects a line, substitute the expression for (y) from the line equation into the quadratic equation and solve for ( x ).
Quadratic equations are fundamental in many areas of mathematics and physics. Understanding their properties and methods of solution is crucial for a variety of applications.
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