Math

Question 1

𝟒𝒙^𝟐 + 𝟔𝒙 + 2

What type of equation is this?

Answer 1

Quadratic Equation

Question 2

𝒂𝒙^𝟐 + 𝒃𝒙 +𝒄 = 0

What do you call the descending order of term according to its degree?

Answer 2

Standard Form

Question 3

If 𝑥^2 = 𝑎 and 𝑎 ≥ 0, then 𝑥 = ±√𝑎.

Answer 3

SQUARE ROOT PROPERTY

Question 4

STEPS in Solving by SQUARE ROOT PROPERTY

Answer 4

1. ISOLATE the squared variable or expression using properties of equality.
2. USE the Square Root Property by getting the square root of both sides.
3. SIMPLIFY if possible.

Question 5

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

Answer 5

perfect square trinomial

Question 6

If ab = 0, then a = 0 and b = 0

Answer 6

ZERO PRODUCT PROPERTY

Question 7

FACTORING (ZERO PRODUCT PROPERTY) STEPS

Answer 7

1. WRITE the equation in standard form (𝑎𝑥2 + 𝑏𝑥+c=0).
2. FACTOR OUT the left side of the equation. (GCF, PST, NPST)
3. EQUATE each factor to zero using the Zero Property.
4. SOLVE for the variable of each equation.

Question 8

STEPS in Solving by QUADRATIC FORMULA

Answer 8

1. WRITE the quadratic equation in standard form
2. IDENTIFY the values of the coefficients a, b and c.
3. SUBSTITUTE the values to the quadratic formula.
4. SIMPLIFY the result.

Question 9

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

Answer 9

Imaginary numbers

Question 10

𝐷 = 𝑏^2 − 4𝑎c

Answer 10

DISCRIMINANT

Question 11

(i) D > 0 (Positive Value)

Answer 11

Real and Unequal

Question 12

(Perfect Square)

Answer 12

Rational

Question 13

(Non-Perfect Square)

Answer 13

Irrational

Question 14

(ii) D = 0

Answer 14

Rational and Equal

Question 15

(iii)D < 0 (Negative Value)

Answer 15

Imaginary and Unequal

Question 16

Quadratic Equations Given the Roots (equation)

Answer 16

𝑥^2 − (𝑆𝑢𝑚)𝑥 + (𝑃𝑟𝑜𝑑𝑢𝑐𝑡) = 0

Question 17

It is an equation in fractional form with some variables in the denominator. It is sometimes known as fractional equation.

Answer 17

Rational Equation

Question 18

If 𝒂/𝒃=𝒄/𝒅, then 𝒂𝒅 = 𝒃𝒄 where a, b, c and d are polynomials.

Answer 18

cross-product property

Question 19

1. Find the LCD.
2. Multiply both sides of the equation by the Least Common Multiple (LCM) of all
   denominators.
3. Write the resulting quadratic equation in standard form.
4. Use any method to solve for the value of any variable.

Answer 19

Steps in Solving Rational Equations

Question 20

Relating amount of work that two or more persons can finish the task together or separately.

Answer 20

Work Problem

Question 21

𝑸 = 𝒓𝒕
where Q= quantity of work
r=rate of work
t= time worked

Answer 21

Work Problem