Page 21 - CHAPTER 4 (Quadratic equations)

CHAPTER 4
QUADRATIC EQUATIONS

Solved examples

3
Therefore. the solutions of the equations are x= and 1.
2
Let us verify our solutions.

2
3
3
3
2
putting x= in 2x -5x+3=0, we get 2 ( ) -5 ( ) +3=0, which is correct.
2 2 2
Similarly, you can verify that x=1 also satisfies the given equation.
Example 1: we divided the equation 2x -5x + 3=0 throughout by 2 to
2
5
3
2
get x - x+ to make the first term a perfect square and then
2 2
completed the square. Instead, we can multiply throughout by 2 to

2
2
make the first term as 4x =(2x) and then complete the square.
This method is illustrated in the next example.

Example 2 : Find the roots of the equation 5x -6x - 2 = 0 by the method
2
of completing the square.

Solution : Multiplying the equation throughout by 5, we get

2
25x -30x-10=0
This is same as

2
2
2
(5x) -2×(5x)×3+3 -3 -10=0
2
i.e (5x-3) -9-10=0
2
i.e (5x-3) -19=0
2
i.e (5x-3) =19

i.e., 5x-3=±√19

i.e., 5x=3±√19

i.e., x= 3±√19
5

Therefore , the roots are 3+√19 and 3-√19
5 5

Verify that the roots are 3+√19 and 3-√19
5 5

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