Kvadratická faktoring kalkulačka

Factorizing a kvadratická na CASIO kalkulačka

`PREREQUISITES`
// Make sure you can code using your calculator.
// > is -> , store, or STO
// x is times
// / is divide (oops.)

`CONTENTS`
Prerequisites						| Line 001
Contents 							| Line 007
Section 1 - Finding Roots 			| Line 021
Section 1 - Factorization 			| Line 029
Section 2 - Expanding     			| Line 033
Section 3 - Sum and Product 		| Line 048
Section 4 - Remainder Theorem 		| Line 068
Coming Up - Turning Point Theorem   | Under construction


The quadratic: ax^2 + bx + c 
`SECTION 1. Basic Quadratic`
// 1. FINDING ROOTS (and factorization) 
In some types of calculator, simply press FUNC 0 1 , then put down the coefficents accordingly.
You should get the 2 roots (press EXE to go to the second root.)

Program:
? > A : ? > B : ? > C : 
( - B + B ^2 - 4 A C ) / 2 A show
( - B - B ^2 - 4 A C ) / 2 A show

Note: Factorized quadratic = (x-a)(x-b), where a and b are roots. (Just negate the values)
Note: Switch to CMPLX mode if you need complex numbers.

`SECTION 2. Expanding`
// 2. EXPANDING A FACTORISED FORM
The factorised form: (ax+b)(cx+d)

Program:
? > A : ? > B : ? > C : ? > D : 
A C show 
A D + B C show 
B D show 

Example Question: Expand (2x+3y)(4x-7y)
Input: A = 3, B = 2, C = 4, D = -7
Output: 12, -13, -14
Answer: 12x^2 - 13xy -14y^2

`SECTION 3. Sum and Product`
// 3A. SUM AND PRODUCT, GIVEN COEFFICIENTS

Program:
? > A: ? > B : ? > C :
- B / A show 
C / A show 

// 3B. GIVEN SUM AND PRODUCT, FORM A QUADRATIC
X = sum
Y = product

Program:
? > X : ? > Y : 
1 show - X show Y show

i.e. the ratio of A : B : C  = 1 : -X : Y

Note: 3A and 3B are recommended to be done by hand.

`SECTION 4. Remainder Theorem`
// 4A. REMAINDER THEOREM: SUBSTITUTION, FIND RESULT

Program:
? > A : ? > B : ? > C : ? > X :
A X ^2 + B X + C show

// 4B. REMAINDER THEOREM: GIVEN VALUE, FIND MISSING TERM (a, b or c)

Program:
? > M : ? > X : 
If M = 0 : Then ? > B : ? > C : sqrt( X - B X - C ) show : IfEnd
If M = 1 : Then ? > A : ? > C : X - A X ^2 - C show : IfEnd
If M = 2 : Then ? > A : ? > B : X - A X ^2 - B show : IfEnd

Note: For degree 1 polynomials, use code 4C to get the value of D, then plot it in X.

// 4C. REMAINDER THEOREM: DEGREE 1 POLYNOMIAL SUBSTITUTION (Xa+Y), FIND RESULT

Program: 
? > A : ? > B : ? > C : ? > X : ? > Y :
- Y / X > D : 
A D ^ 2 + B D + C show