Let’s discuss each topic of Quadratic Equations Class 10 one-by-one

Roots of Quadratic Equation

Therefore, 1 is a solution of this equation.
Try and solve a previous boards question based on this topic:

Methods of Solving Quadratic Equation

A quadratic equation can be solved using: – Factorisation – Quadratic Formula – Method of completing squares. Lets revise these methods:

1. Factorisation
We all know how to factorise a quadratic polynomial. We have learnt this in Polynomials chapter.

Note that roots of a quadratic equation ax^2 + bx + c = 0 are same as zeros of quadratic polynomial ax^2 + bx + c

Let’s take a look at an example:

2. Quadratic Formula: 

Roots of any quadratic equation ax^2 + bx + c = 0 can be given by

3. Method of completing squares:

By adding and subtracting a suitable constant, we club the x^2 and x terms in the quadratic equation to get a perfect square term, and solve for x.
Example:

Till now, in boards, no particular method has been specified to solve a question. You can use the method you are most comfortable with.

Nature of Roots of Quadratic Equations

The nature of roots of a quadratic equation can be identified from the discriminant of the equation. A quadratic equation has

1. Two distinct real roots, if D > 0
2. Two equal real roots, if D = 0
3. No real roots, if D < 0

You should remember these conditions as at least one question in boards definitely comes on this concept. Lets look at a few questions that are asked in exam based on this concept:

Word Problems

There is a high probability of getting word problem worth 4 marks from this chapter. The concepts on which the questions are asked are:

1. Work done
2. Speed – distance & time
3. Cost of articles
4. Age problems and similar real-life application based questions.

Always analyse statements in word problems carefully before forming equations. Lets look at an example of question that comes on this concept:

Previous Year Questions

Let’s solve one of the questions: