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Proper, Improper and Mixed Fractions
Fractional Arithmetic
Changing the Subject of an Expression
Multiplying Expressions
Factorising Quadratic Expressions
Ex. 0:
-6 x2 + -5 x + 7 = 0
=>
(x -
5 + √193
-12
) (x -
5 - √193
-12
)
Ex. 1:
-5 x2 + -5 x + -4 = 0
=>
No real roots
(x -
5 + i √55
-10
) (x -
5 - i √55
-10
)
Ex. 2:
1 x2 + 7 x + -9 = 0
=>
(x -
-7 + √85
2
) (x -
-7 - √85
2
)
Ex. 3:
-3 x2 + 2 x + -9 = 0
=>
No real roots
(x -
-2 + i √104
-6
) (x -
-2 - i √104
-6
)
Ex. 4:
-3 x2 + -8 x + 9 = 0
=>
(x -
8 + √172
-6
) (x -
8 - √172
-6
)
Ex. 5:
4 x2 + -8 x + 9 = 0
=>
No real roots
(x -
8 + i √80
8
) (x -
8 - i √80
8
)
Ex. 6:
-7 x2 + 2 x + -7 = 0
=>
No real roots
(x -
-2 + i √192
-14
) (x -
-2 - i √192
-14
)
Ex. 7:
6 x2 + -2 x + 7 = 0
=>
No real roots
(x -
2 + i √164
12
) (x -
2 - i √164
12
)
Ex. 8:
-5 x2 + -8 x + -3 = 0
=>
(x -
1
-1
) (x -
3
-5
)
Ex. 9:
-7 x2 + -8 x + 6 = 0
=>
(x -
8 + √232
-14
) (x -
8 - √232
-14
)