Solving Quadratic Equations
Solving Quadratic Equations x squared, x’s, number equals zero SOLVE
x 2 5 x + 6 0
Can we FACTORISE ? (x
Factorised (as shown earlier)
)(x
(x
x
Solved
2 )(x
- 2 0
x 2
) 0
Guide number 6 1x6 2x3
3) 0
x
- 3 0
x 3
Remember Our Golden Rule
Get all the terms to the LHS of the equals, with zero on the RHS
Add to 7 No Good Add to 5 Yes! Perfect
Solving Quadratic Equations x squared, x’s, number equals zero SO LV E
x 2 6 x + 5 0
Can we FACTORISE ?
Factorised
Solved
(x
)(x
(x
1) ( x
x
+ 1 0
x 1
What if the last sign of the equation is a MINUS?
) 0
Guide number 5 1x5
Add to 6 Yes.
5) 0
x
+ 5 0 x 5
ax2 bx c 0
Solving Quadratic Equations x squared, x’s, number equals zero SO LV E
x 2 x - 2 0 0
Can we FACTORISE ? )(x
) 0
4) ( x
5) 0
(x
Factorised
(x
x
Solved
- 4 0
x 4
x
Guide number 20 1x20 2x10 4x5
+ 5 0
x 5
Remember Our Golden Rule
Subtract to 19 No Good Subtract to 8 No Subtract Good either to 1 Yes! Perfect
Solving Quadratic Equations x squared, x’s, number equals zero x 2 5 x - 1 4 0
SOLVE
Can we FACTORISE ? (x
Factorised
)(x
(x
x
Solved
2 )(x
+ 2 0
x 2
) 0 7) 0
x
- 7 0 x 7
Guide number 14 1x14 2x7
Subtract to 13 No Good Subtract to 5 Yes! Perfect
When it’s not in the correct form to solve
SOLVE
x2 4 x 12
What’s different about how this equation looks? Is it still a Quadratic Equation? We need it in the correct FORM before we start
x2 4x 4x 12 4x x2 4x 12 x2 4x 12 12 12 x2 4x 12 0 Remember Rule Now we canOur startGolden solving……
Get rid of 4x and -12 on the RHS
Solving Quadratic Equations x squared, x’s, number equals zero SOLVE
x 2 4 x - 1 2 0
Can we FACTORISE ? (x
Factorised
)(x
(x
x
Solved
2) ( x
+ 2 0
x 2
) 0
6) 0
x
Guide number 12 1x12 2x6 3x4
6 0 x 6
Remember Our Golden Rule
Subtract to 13 No Good Subtract to 4 Yes. Perfect!
WHAT YOU MUST KNOW Get the equation in the form x squared, x’s, number equals zero
Golden Rule
ax2
bx
c
0
ax2
bx c 0
Plus
Minus
Your factors of c must add to the middle number (b)
Your factors of c must subtract to the middle number (b)
WHAT YOU MUST DO Practise Practise Practise SO LV E
x2 4x 4 0
SOLVE
x2 x 6 0
SOLVE
x2 16 x 63
SOLVE
5x x2 36
SOLVE
x2 3x 4 0
SOLVE
x2 17 x 70 0
Get all the terms to the LHS of the equals, with zero on the RHS or
Get the equation in the form x squared, x’s, number equals zero
x 2 5 x + 6 0
Can we FACTORISE ? (x
Factorised (as shown earlier)
)(x
(x
x
Solved
2 )(x
- 2 0
x 2
) 0
Guide number 6 1x6 2x3
3) 0
x
- 3 0
x 3
Remember Our Golden Rule
Get all the terms to the LHS of the equals, with zero on the RHS
Add to 7 No Good Add to 5 Yes! Perfect
Solving Quadratic Equations x squared, x’s, number equals zero SO LV E
x 2 6 x + 5 0
Can we FACTORISE ?
Factorised
Solved
(x
)(x
(x
1) ( x
x
+ 1 0
x 1
What if the last sign of the equation is a MINUS?
) 0
Guide number 5 1x5
Add to 6 Yes.
5) 0
x
+ 5 0 x 5
ax2 bx c 0
Solving Quadratic Equations x squared, x’s, number equals zero SO LV E
x 2 x - 2 0 0
Can we FACTORISE ? )(x
) 0
4) ( x
5) 0
(x
Factorised
(x
x
Solved
- 4 0
x 4
x
Guide number 20 1x20 2x10 4x5
+ 5 0
x 5
Remember Our Golden Rule
Subtract to 19 No Good Subtract to 8 No Subtract Good either to 1 Yes! Perfect
Solving Quadratic Equations x squared, x’s, number equals zero x 2 5 x - 1 4 0
SOLVE
Can we FACTORISE ? (x
Factorised
)(x
(x
x
Solved
2 )(x
+ 2 0
x 2
) 0 7) 0
x
- 7 0 x 7
Guide number 14 1x14 2x7
Subtract to 13 No Good Subtract to 5 Yes! Perfect
When it’s not in the correct form to solve
SOLVE
x2 4 x 12
What’s different about how this equation looks? Is it still a Quadratic Equation? We need it in the correct FORM before we start
x2 4x 4x 12 4x x2 4x 12 x2 4x 12 12 12 x2 4x 12 0 Remember Rule Now we canOur startGolden solving……
Get rid of 4x and -12 on the RHS
Solving Quadratic Equations x squared, x’s, number equals zero SOLVE
x 2 4 x - 1 2 0
Can we FACTORISE ? (x
Factorised
)(x
(x
x
Solved
2) ( x
+ 2 0
x 2
) 0
6) 0
x
Guide number 12 1x12 2x6 3x4
6 0 x 6
Remember Our Golden Rule
Subtract to 13 No Good Subtract to 4 Yes. Perfect!
WHAT YOU MUST KNOW Get the equation in the form x squared, x’s, number equals zero
Golden Rule
ax2
bx
c
0
ax2
bx c 0
Plus
Minus
Your factors of c must add to the middle number (b)
Your factors of c must subtract to the middle number (b)
WHAT YOU MUST DO Practise Practise Practise SO LV E
x2 4x 4 0
SOLVE
x2 x 6 0
SOLVE
x2 16 x 63
SOLVE
5x x2 36
SOLVE
x2 3x 4 0
SOLVE
x2 17 x 70 0
Get all the terms to the LHS of the equals, with zero on the RHS or
Get the equation in the form x squared, x’s, number equals zero
