Quadratic Equations Class 10 – Continuing our series for Class 10 Revision for CBSE board exams, we bring you a new chapter today i.e. Quadratic equations. Every year, this chapter comes for 4 – 7 marks in boards.
If you analyse the previous year boards questions, you can observe that questions on discriminant and roots of equation and their nature are asked for 1 or 2 marks while solving quadratic equations to find roots and word problems are asked for 3 or 4 marks.
Concepts to be covered during this revision session of Quadratic Equations Class 10
- Roots of Quadratic Equation
- Methods of solving Quadratic Equation: – Factorisation – Quadratic Formula – Method of completing squares
- Nature of roots of quadratic equations
- Word Problems
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:
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.
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
- Two distinct real roots, if D > 0
- Two equal real roots, if D = 0
- 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:
There is a high probability of getting word problem worth 4 marks from this chapter. The concepts on which the questions are asked are:
- Work done
- Speed – distance & time
- Cost of articles
- 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:
Let’s solve one of the questions: