Quadratic Equation Class 10 Notes: Chapter 4

Quadratic equations class 10 notes i.e. for chapter 4 provided here can help the class 10 students to prepare this topic in a more effective way and revise the concepts easily. The important points from this chapter which are highlighted here include-

  • What is a quadratic equation?
  • Roots of a quadratic equation
  • Solution of a quadratic equation
  • Example questions
  • Practice questions
  • Articles related to quadratic equations

What is a Quadratic Equation?

A polynomial having the degree of 2 is said to be a quadratic equation. The general representation of quadratic equation is given as \(ax^{2} + bx + c = 0\), where \(a \neq 0\).

Roots of a Quadratic Equation

A quadratic equation is suppose to have two roots (say \(\alpha\) and \(\beta\)) that will satisfy the equation and result in the value of \(p(\alpha) = p(\beta) = 0\)

Quadratic Formula

For a quadratic equation \(ax^{2} + bx + c = 0\), the roots are given by the following formula-

\(\frac{-b\pm \sqrt{b^{2}-4ac}}{2a},\, provided,\,b^{2}-4ac\geq 0\)

This method is called solving quadratic equation using the quadratic formula.

Important Notes:

A quadratic equation will have:

  • Two distinct roots, if \(b^{2}-4ac> 0\)
  • Coincident roots i.e. two equal roots, if \(b^{2}-4ac= 0\)
  • No real roots, if \(b^{2}-4ac< 0\)

Solution of a Quadratic Equation

The solution of a quadratic equation is the other term for a root of a quadratic equation. Apart from the quadratic formula mentioned above, the root or the solution of a quadratic equation can be found out by two methods which are-

  • The solution of a Quadratic equation by Factorization
  • The solution of a Quadratic Equation by Completing the Square Method

Solution of Quadratic equation by Factorization

solution of a Quadratic equation by Factorization

Solution of Quadratic Equation by Completing the Square Method

Consider the Expression \(x^{2} + 4x\).

Quadratic Equation For Class 10

Let us understand the method of completing the square pictorially.

The process is as follows-

\(x^{2} + 4x = \left ( x^{2} +\frac{4}{2}x \right ) + \frac{4}{2}x\) \(= x^{2} + 2x + 2x\) \(= (x+2)x + 2 \times x\) \(= (x+2)x + 2 \times x + 2 \times 2 – 2 \times 2\) \(= (x+2) \times (x+2) – 2 \times 2\) \(= (x+2)^{2} – 4\)

This method is known as the method of completing the square.

Quadratic Equation For Class 10

Practice Question

  1. Find the value of “k” for the equation \(2x^{2}+kx+3=0\)
  2. Is it possible to build a rectangular field of perimeter 80 m and area 400 m2? If so, find its length and breadth.
  3. Find the discriminant of the equation \(3x^{2}-2x+\frac{1}{3}=0\) and find
    the nature of its roots. Find them, if they are real.

Access CBSE Class 10 Maths Sample Papers Here.

Access NCERT Class 10 Maths Book Here.

Related Quadratic Equations Articles for Class 10

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Practise This Question

Find the value of k for which x24x+k=0 has coincident roots.