Page 1 - LN

SAI International School
CLASS - X

Mathematics
CHAPTER- 4: Quadratic Equation -2

Lesson Notes-2

SUBTOPIC : Solving Quadratic Equations by Factorisation

Solution or root of Quadratic Equation
The values of x for which a quadratic equation is satisfied are called the roots or
solutions of the quadratic equation.
2
2
If α is a root of the quadratic equation ax +bx+c = 0, then, aα +bα+c=0.
2
2
Zero of the polynomial ax +bx+c is same as the root of the equation ax +bx+c = 0
2
Example 1. Find if x = 1 is a root of the quadratic equation 3x - 2x - 1 = 0
2
Ans: The given quadratic equation is 3x - 2x - 1 = 0
Substituting x = 1 on the LHS of the given equation, we get,
2
LHS = 3 (1) - 2 (1) - 1
= 3 - 2 - 1
= 3 - 3
= 0
= RHS
Hence, x = 1 is a solution of the given quadratic equation.

Example 2: Find the value of k for which x = - a is a solution of the given
2
equation x + 3ax + k = 0
2
Ans: Since x = - a is a root of the given equation, x + 3ax + k = 0,
2
Therefore, it must satisfy the equation (-a) + 3a(-a) + k = 0
2
2
a - 3a + k = 0
2
-2a + k = 0
2
k = 2a

A quadratic equation can have two distinct real roots, two equal real roots or real roots
may not exist.

1