HOW TO SOLVE REDUCIBLE QUADRATIC EQUATIONS

1. SUBJECT : MATHEMATICS
CHAPTER ( 2/4 ) : EQUATIONS
LESSON NO : 04 OF 09
TOPIC : SOLUTION OF
EQUATIONS REDUCIBLE
TO QUADRATIC
EQUATION

3. Q. What do you mean by an equation ?
A. An equation is a statement in which two quantities are
equal.
Q. What do you mean by quadratic equation?
A. An equation in one variable and maximum power of
that variable is two is called quadratic equation.
Q. How many techniques to solve quadratic equations?
A. There are three basic techniques to solve a quadratic
equation:
(i) Factorization method
(ii) Completing square method
(iii) Quadratic formula

4. SOLUTION OF EQUATIONS REDUCIBLE
TO QUADRATIC EQUATION
 First Form
 Second Form
0
fx
e
dx
c
bx
a






fd,b,x 
c
y
b
ay  0y 

5. Solve
Solution
Multiplying both sides by (x + 1) (x-1)
5 (x-1) +3 (x+1) = 6 (x+1)(x-1)
5x – 5 + 3x + 3 = 6x2 – 6
6
1x
3
1x
5




Example
SOLUTION OF EQUATIONS REDUCIBLE
TO QUADRATIC EQUATION

6. 8x – 2 = 6x2 – 6
6x2 - 8x – 6+ 2 = 0
6x2 – 8x – 4 = 0
3x2 - 4x – 2 = 0
SOLUTION OF EQUATIONS REDUCIBLE
TO QUADRATIC EQUATION
We Know that
a2
ac4bb
x
2



7.   
6
234164
x


6
24164
x


3
102
6
404
x




SOLUTION OF EQUATIONS REDUCIBLE
TO QUADRATIC EQUATION
Putting the values of co- efficient in the formula

8. Solution
Let
14x
14x
y



Then the given equation can be written in the form
3
10
y
1
y 
SOLUTION OF EQUATIONS REDUCIBLE
TO QUADRATIC EQUATION
3
1
3
14x
14x
14x
14x






Example
Solve
(i)

9. 3y2 – 10y + 3 = 0
3y2 – 9y – y + 3 = 0
3y(y-3) - 1(y – 3) = 0
(3y – 1)(y – 3) = 0
(3y –1) = 0 and (y – 3) = 0
SOLUTION OF EQUATIONS REDUCIBLE
TO QUADRATIC EQUATION

10. 3
1
y  or y = 3
Now by substituting the values of y in (i), we have
3
1
14x
14x



3
14x
14x



and
2
1
x 
2
1
x

and
Therefore the solution set is






2
1
,
2
1
SOLUTION OF EQUATIONS REDUCIBLE
TO QUADRATIC EQUATION

11. SOLUTION OF EQUATIONS REDUCIBLE TO
QUADRATIC EQUATION
 First Form
 Second Form
0
fx
e
dx
c
bx
a






fd,b,x 
c
y
b
ay  0y 

13. Assignment
1,0x;
2
5
x
1x
1x
x




4
17
13x
1
13x 


(a)
(b)
SOLUTION OF EQUATIONS REDUCIBLE
TO QUADRATIC EQUATION

14. SOLUTION OF EQUATIONS
REDUCIBLE TO QUADRATIC FORM