Quadratic equations

Let’s recap first:

Linear equations

1. Usually only 1 unknown.
2. Highest power is 1

Solve them by: 

1. If there are fractions find the LCD
2. Multiply all terms on both sides of the equation by the LCD
3. Simplify further by removing brackets
4. Move all terms with variable to left of = sign by performing inverse operations
5. Move all constant terms to right of = sign by performing inverse operations
6. Add or subtract like terms
7. Divide both sides by the co- efficient of the variable

Quadratic equations

1. At least one term has a variable that is squared
2. No term is greater than power of 2
3. Standard form is: ax² + bx + c = 0
4. Has two roots (or possible solutions) because if a x b = 0 then either a= 0 or b=0 or both a and b =0 [Called the null factor law]

Solve by:

1. Write in standard form

2. Factorise trinomial

3. Find the values for the variable

Example 1

4x² -1 = 7x

⇒ 4x² – 7x -1 = 0

⇒ 4x² -4x -3x -1 = 0                                 [Split middle term]

⇒ 4x (x -1) -3 (x-1) =0

⇒ (4x -3) (x-1) =0                                   [Remove 1 of the repeated terms]

⇒ x = ¾ OR x = 1

Example 2

b² – 17 = 1

⇒ b2 -16 = 0                                            [Difference of squares]

⇒(b-4) (b+4) =0

⇒ b = 4 OR b= -4

Example 3

(b-7) -3 = (-b+5)

⇒ (b-7)(b-5) = 3

⇒ b² – 7b -5b +35 -3 = 0

⇒ b² -12b + 32 =0

⇒ (b -8) (b-4) = 0

⇒ b=8 OR b=4

Coming next: Exponential equations!