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Title: Quadratic Equation and Factorise
Description: Notes for teaching you about quadratic equation and factorisation
Description: Notes for teaching you about quadratic equation and factorisation
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1
...
02
...
3a
1
...
a) 3x + 6x = 0
[By taking out the HCF 3x]
b) 5x – 35x = 0
[By taking out the HCF 5x]
c) 5x – 65 = 0
[By taking out the HCF 5]
d) 7x + 42 =
[By taking out the HCF 7]
2
2
2
2
0
2
...
a) x – 25 = 0
2
[First, express as a difference of two squares]
[Then, factorise using the formula:
a – b = (a – b) (a + b)]
2
2
b) 3x – 48 = 0
2
[First, take out the HCF 3]
[Then, express as a difference of two
squares]
[Finally, factorise using the formula:
a – b = (a – b) (a + b)]
2
2
3
...
a) 4x – 9 = 0
2
[First, express as a difference of two
squares]
[Then, factorise using the formula:
a – b = (a – b) (a + b)]
2
b) 121 x – 100 = 0
2
2
[First, express as a difference of two
squares]
[Then, factorise using the formula:
a – b = (a – b) (a + b)]
2
2
4
...
a
...
x - 7x + 6 = 0
Side Working
c
...
x + 2x – 3 = 0
Side Working
2
2
2
2
e)
4x + 12x + 9 = 0
Side Working
f)
9x – 12 x + 4 = 0
Side Working
2
2
Home Work
Exercise 1
...
Solve the following quadratic equations by Factorisation
using the difference of two squares formula
...
7x + 14x = 0
2
b) 8x – 18 = 0
2
c) 3x – 192 = 0
2
[General Form]
[First, take out the HCF 3]
[Then, express as a difference of two
squares]
[Next, factorise using the formula:
a – b = (a – b) (a + b)]
2
2
d) 18 x – 32 = 0
2
[First, take out the HCF
2]
[Then, express as a difference of two
squares]
[Next, factorise using the formula:
a – b = (a – b) (a + b)]
2
e) - 2x + 50 = 0
2
f) 27x – 192 = 0
2
2
2
...
2x – 14x + 12 = 0
2]
2
[First, take out the HCF
Side Working
c) 5x – 35x – 40 = 0
2
[First, take out the HCF
5]
Side Working
d) 27x - 36x + 12 = 0
2
End of Question Paper
Sub Topic: 1
...
3 Solving Quadratic Equations by Factorisation
...
3
...
- ax + bx + c = 0
2
Roots of Quadratic Equations
i) The root of a quadratic equation is the value of the variable
x
which satisfies the equation
...
iii) A given quadratic equation may have:
a
...
Two real roots which are distinct (real and different)
c
...
Factorised Form with the RHS equal 0
...
General Form: ax + bx + c = 0
2
v)
For examples:
1
...
a) 3x (x + 2) = 0 [Factorised Form with 0 on the RHS]
Hence, 3x = 0 or x + 2 = 0 [By letting each factor be 0]
x = 0 or x = - 2
Ans: The roots are 0 and – 2
...
(x – 2) (x + 5) = 0 [Factorised Form with 0 on the RHS]
Hence, x – 2 = 0 or x + 5 = 0[By letting each factor be 0]
x = 2
or x = - 5
Ans: The roots are 2 and – 5
...
Solve the following quadratic equations by using
the difference of two squares formula
...
2
2
2
2
2
3 x – 48 = 0
[General Form]
3 (x – 16) = 0 [First, take out the HCF 3]
3 (x – 4 ) = 0 [ Then, express as a difference of two
squares]
3 (x – 4) (x + 4) = 0 [Next, factorise using the formula:
a – b = (a – b) (a + b)]
Hence, x – 4 = 0 or x + 4 = 0[By letting each factor be 0]
x = 4 or
x = -4
Ans: The roots are 4 and – 4
b)
2
2
2
2
2
2
3
...
a
...
121 x – 100 = 0
[General Form]
(11x) – 10 = 0 [First, express as a difference of two squares]
(11x – 10) (11x + 10) = 0 [Then, factorise using the formula:
a – b = (a – b) (a + b)]
Hence, 11x – 10 = 0 or 11x + 10 = 0[By letting each factor
be 0]
11x = 10 or 11x = - 10
x = 10/11 or
x = - 10/11
Ans: The roots are 10/11 and - 10/11
2
2
2
2
2
4
...
a) x + 5x + 6 = 0 [General Form]
(x + 2) (x + 3) = 0 [Factorised Form]
Hence, x + 2 = 0 or x + 3 = 0
3x
x = - 2 or
x=-3
Ans: The roots are – 2 and – 3
...
2
c) x - 7x – 8 = 0 [General Form]
2
x + 6
2
+ 5x
2
Side Working
(x – 8) (x + 1) = 0 [Factorised Form]
Hence, x – 8 = 0 or x + 1 = 0
x = 8 or x = - 1
Ans: The roots are 8 and – 1
d) x + 2x – 3 = 0
[General Form]
(x + 3) (x – 1) = 0 [Factorised Form]
Hence, x + 3 = 0 or x – 1 = 0
x = - 3 or
x = 1
...
2
e) 4x + 12x + 9 = 0 [General Form]
(2x + 3) (2x + 3) = 0 [Factorised Form]
Hence, 2x + 3 = 0 or 2x + 3 = 0
2x = - 3 or 2x = - 3
2
x–8
x+1
x– 8
- 8x
+1x
- 7x
2
Side Working
x+ 3
+3x
x– 1
- 1x
x –3
+2x
2
Side Working
2x + 3
+ 6x
2x + 3
+ 6x
4x + 9
+12x
2
Title: Quadratic Equation and Factorise
Description: Notes for teaching you about quadratic equation and factorisation
Description: Notes for teaching you about quadratic equation and factorisation