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Quadratic Equation class 10 notes|class 10 Maths chapter 4 notes|CBSE class 10 Maths notes |

February 15, 2022

 QUADRATIC EQUATIONS


Topics to be covered:

  • Quadratic Polynomial.
  • Quadratic equation.
  • Types of quadratic equation.
  • Roots of a quadratic equation.
  • Methods for solving the quadratic equation.
  • Nature of roots.
QUADRATIC POLYNOMIAL

  • A polynomial of degree 2 is known as Quadratic polynomial.
  • It is in the form of P(x)=ax2+bx+c, a≠0
QUADRATIC EQUATION

  • A quadratic equation in the variable x is an equation of the form ax2+bx+c, where a, b and c are real numbers and a≠0 is called a quadratic equation.
  • Standard form-ax2+bx+c.
TYPES OF QUADRATIC EQUATION

  1. Complete quadratic equation-ax2+bx+c,where a, b and c are real numbers and a≠0 .
  2. Pure quadratic equation-ax^2=0.

METHODS TO SOLVE THE QUADRATIC EQUATION

There are three methods for solving quadratic equation:

(a) By factorization

(b) By completing the square

(c) By Quadratic Formula

(A) Factorisation Method:

-In this method we factorise the equation into two linear factor and equate  each factor to zero to find the root of the given equation.

Step 1 - Given quadratic equation in the form of ax2+bx+c.

Step 2-  split the middle term BX as  MX + NX so that the sum of m and n is equal to (b) and sum of product of n and m is equal to a×c.

Step 3-  by Factorisation we get two linear factors (x+p)and (x+q).

Step 4- Now we have to equate fector  to zero to find the value of x.

Example-

x2 – 3x – 10 = 0

⇒ x2 - 5x + 2x - 10 = 0

⇒ x(x - 5) + 2(x - 5) = 0

⇒ (x - 5)(x + 2) = 0

Roots of this equation are the values for which (x - 5)(x + 2) = 0∴ x - 5 = 0 or x + 2 = 0⇒ x = 5 or x = -2

(B) COMPLETING THE SQUARE METHOD

-In this method we convert the equation in the square form of(x + a)2 — b2 = 0 to find the roots. 

Step 1- We have given a quadratic equation in the form of ax2+bx+c.

Step 2- Divide the quadratic equation by the coefficient of x square. i.e a.


Step 3- Transfer the constant on RHS then add square of the half of the coefficient of x to  both sides.


Step 4- Now write lhs perfect square and simplifies the RHS. 


Step5- Take the square root on RHS-

Step 6- Move all the constant term to RHS and then we can calculate the value of  x as there is no variable at RHS-

Step 7- By calculating further we get a formula which is known as Quadratic Formula.

NATURE OF ROOTS

-Based on the value of the discriminant, D=b2−4ac, the roots of a quadratic equation can be of three types.

Case 1: If D>0, the equation has two distinct real roots.

Case 2: If D=0, the equation has two equal real roots.

Case 3: If D<0, the equation has no real roots [ Imagery Roots].


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Chapter : Quadratic Equation

  1. HANDRITTEN NOTES
  2. NCERT SOLUTIONS
  3. NCERT EXAMPLER
  4. CASE STUDY
  5. PYQs