Math Flashcards
𝟒𝒙^𝟐 + 𝟔𝒙 + 2
What type of equation is this?
Quadratic Equation
𝒂𝒙^𝟐 + 𝒃𝒙 +𝒄 = 0
What do you call the descending order of term according to its degree?
Standard Form
If 𝑥^2 = 𝑎 and 𝑎 ≥ 0, then 𝑥 = ±√𝑎.
SQUARE ROOT PROPERTY
STEPS in Solving by SQUARE ROOT PROPERTY
- ISOLATE the squared variable or expression using properties of equality.
- USE the Square Root Property by getting the square root of both sides.
- SIMPLIFY if possible.
If the first and last terms are perfect squares and the middle term is twice the product of
the roots of the first and last terms.
Example: 𝑥^2 + 12𝑥 + 36
perfect square trinomial
If ab = 0, then a = 0 and b = 0
ZERO PRODUCT PROPERTY
FACTORING (ZERO PRODUCT PROPERTY) STEPS
- WRITE the equation in standard form (𝑎𝑥2 + 𝑏𝑥+c=0).
- FACTOR OUT the left side of the equation. (GCF, PST, NPST)
- EQUATE each factor to zero using the Zero Property.
- SOLVE for the variable of each equation.
STEPS in Solving by QUADRATIC FORMULA
- WRITE the quadratic equation in standard form
- IDENTIFY the values of the coefficients a, b and c.
- SUBSTITUTE the values to the quadratic formula.
- SIMPLIFY the result.
These are unreal numbers, denoted by i, which the value does not
exist. Such numbers are the square root of negative numbers.
𝑖 = √−1 𝑎𝑛𝑑 𝑖^2 = −1
Imaginary numbers
𝐷 = 𝑏^2 − 4𝑎c
DISCRIMINANT
(i) D > 0 (Positive Value)
Real and Unequal
(Perfect Square)
Rational
(Non-Perfect Square)
Irrational
(ii) D = 0
Rational and Equal
(iii)D < 0 (Negative Value)
Imaginary and Unequal
Quadratic Equations Given the Roots (equation)
𝑥^2 − (𝑆𝑢𝑚)𝑥 + (𝑃𝑟𝑜𝑑𝑢𝑐𝑡) = 0
It is an equation in fractional form with some variables in the denominator. It is sometimes known as fractional equation.
Rational Equation
If 𝒂/𝒃=𝒄/𝒅, then 𝒂𝒅 = 𝒃𝒄 where a, b, c and d are polynomials.
cross-product property
- Find the LCD.
- Multiply both sides of the equation by the Least Common Multiple (LCM) of all
denominators. - Write the resulting quadratic equation in standard form.
- Use any method to solve for the value of any variable.
Steps in Solving Rational Equations
Relating amount of work that two or more persons can finish the task together or separately.
Work Problem
𝑸 = 𝒓𝒕
where Q= quantity of work
r=rate of work
t= time worked
Work Problem
