CAT Equations of the form of ax2 + by +c = 0 - Practice Questions & MCQ

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.