Notesale: Turn your study into money

Document Preview

Extracts from the notes are below, to see the PDF you'll receive please use the links above

---

Quadratic Equations:
Equations with Fractions:
→
→
→
→
→

Factorize denominators
Find a common denominator
(change signs if necessary)
Multiply each term by the LCD &
drop the LCD
Set the equation equal to 0 &
factorize
...
)

The Quadratic Formula:
𝒃 − 𝟒𝒂𝒄
𝟐𝒂
→ Equation must be written in
standard form (𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0)
→ Substitute values into formula to
solve for 𝑥
𝒙=

−𝒃 ±

𝟐

The ‘k’ Method:

To be used when:
→ There is repetition in an equation
→ If 𝑥 is raised to the power of 4
after brackets are multiplied out
...


Completing the Square:

Equations:
→ Divide by the coefficient of 𝑥 2
→ Move the constant to the right
→ Divide the coefficient of 𝑥 by 2 & square it
→ Add this number to both sides of the equation
→ Factorize the left & add up the right
→ Square root both sides
→ Solve for x by adding the right of the equation to
the left & subtracting it from the left
Expressions:
→ Divide the expression by the coefficient of 𝑥 2
→ Place 𝑥 2 & 𝑥 in a bracket, leaving the constant
outside
→ Divide the coefficient of 𝑥 by 2 & square it
→ Add the answer to the bracket & subtract it from the
constant
→ Factorize the trinomial & add the constants
→ Multiply the answer by the original coefficient of 𝑥 2

Quadratic Inequalities:

[included]: ≤; ≥; ○
(excluded): >; <; ●
Place +𝑥 alone on one side
If you divide be a negative, the
direction of the sign changes
→ Label zones, starting from the
RHS +; -; +; → > & ≥ falls in a + zone
→ < & ≤ falls in a - zone
→
→
→
→

Simultaneous Equations:

→ Consist of a linear (𝑎𝑥 + 𝑏 = 0)
equation and of a quadratic
equation (𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0)
→ Set the linear equation equal to
𝑥 or 𝑦
→ Substitute the linear equation
into the quadratic equation
→ Solve for the variable
→ Substitute the answer into the
linear equation for the other
variable
* Remember: check restrictions for
fractions and surds

Nature of Roots:
→ 𝛿 𝑜𝑟 Δ = 𝑏 2 − 4𝑎𝑐

Squaring Both Sides:
→
→
→
→

Simplify the equation to have a square root on one side

---