FACTORISATION INVOLVING ALPHA (α) AND BETA (β)
(1). given that α and β are the roots of the equation 5x2 – 7x + 1 = 0.
What is the value of (α – β)2
(A)29/5 (B)13/5 (C)7/5 (D)29/25
--What is the value of (α + 1)(β + 1)
(A)13/5 (B)27/25 (C)11/5 (D)-7/5
--What is the value of (3α – 1)(3β – 1)
(A)11/5 (B)7/5 (C)-7/5 (D)22/5
Solution:-Using CASIO fx-991MS calculator
Solving the equation 5x2 – 7x + 1 = 0 ------ax2 + bx + c = 0 where a = 5, b = -7, c = 1
Press [ON] [MODE] [MODE] [MODE] [1] [→] [2] [5] [=] [-7] [=] [1] [=] (X1 = 1.238516481) PRESS [=] or [↓] (X2 = 0.161483519) press [MODE] [1], Make x1 = α and x2 = β since the CASIO fx-991MS calculator doesn’t have the α and β sign let α = A and β = B
[AC] [1.238516481] [SHIFT] [STO] [A] (A = 1.238516481)
Note:-Please use the key [AC] during calculations after you press the key [ON] on any question given
[AC] [0.161483519] [SHIFT] [STO] [B] (B = 0.161483519)
What is the value of (α - β)2
(A)29/5 (B)13/5 (C)7/5 (D)29/25
[AC] [(] [ALPHA] [A] [+] [ALPHA] [B] [)] [x2] [=] (1.16000001)
The correct option is “D”
What is the value of (α + 1)(β + 1)
(A)13/5 (B)27/25 (C)11/5 (D)-7/5
[AC] [(] [ALPHA] [A] [+] [1] [)] [(] [ALPHA] [B] [+] [1] [)] [=] (2.6)
The correct option is “A”
What is the value of (3α – 1)(3β – 1)
(A)11/5 (B)7/5 (C)-7/5 (D)22/5
[AC] [(] [3] [ALPHA] [A] [-] [1] [)] [(] [3] [ALPHA] [B] [-] [1] [)] [=] (-1.400000003)
The correct option is “C”
(2). If the roots of the equation 4x2 – 6x – 4 = 0 are α and β find (α + β)2
(A)6/7 (B)21/3 (C)15/8 (D)15/5
What is the value of (α2 + β2)(β2 – 1/α2)
(A)14/7 (B)18/32 (C)17/16 (D)17/10
Solution:-Using CASIO fx-991MS calculator
Solving the equation 4x2 – 6x – 4 = 0 ------ax2 + bx + c = 0 where a = 4, b = -6, c = -4
Press [ON] [MODE] [MODE] [MODE] [1] [→] [2] [4] [=] [-] [6] [=] [-] [4] [=] (X1 = 2) press [=] or [↓] (X2 = -0.5) press [ab/c] (½) press [MODE] [1]
Make x1 = α and x2 = β since the CASIO fx-991MS calculator doesn’t have the α and β sign let α = A and β = B
[AC] [2] [SHIFT] [STO] [A] (A = 0.75)
Note:-Please use the key [AC] during calculations after you press the key [ON] on any question given
[AC] [(-)] [0] [.] [5] [SHIFT] [STO] [B] (B = -0.5)
(α + β)2
(A)6/7 (B)21/3 (C)15/8 (D)9/4
[AC] [(] [ALPHA] [A] [+] [ALPHA] [B] [)] [x2] [=] (2.25) press [SHIFT] [d/c] (9/4)
The correct option is “D”
What is the value of (α2 + β2)(β2 – 1/α2)
(A)14/7 (B)18/32 (C)17/16 (D) 0
[AC] [(] [ALPHA] [A] [x2] [+] [ALPHA] [B] [x2] [)] [(] [ALPHA] [B] [x2] [-] [1] [ab/c] [ALPHA] [A] [x2] [)] [=] (0)
The correct option is “D”
(3). If α and β are the roots of the equation 3x2 + 5x – 2 = 0 find the values of 1/α + 1/β
(A)-5/2 (B)-2/3 (C)1/2 (D)5/2
Solution:-Using CASIO fx-991MS calculator
Solving the equation 3x2 + 5x – 2 = 0 ------ax2 + bx + c = 0 where a = 3, b = 5, c = -2
Press [ON] [MODE] [MODE] [MODE] [1] [→] [2] [3] [=] [5] [=] [-] [2] [=] (X1 = 0.333333333) press [ab/c] (⅓)press [=] or [↓] (X2 = -2) press [ab/c] (½) press [MODE] [1]
Make x1 = α and x2 = β since the Casio fx-991MS calculator doesn’t have the α and β sign let α = A and β = B
[AC] [1] [ab/c] [3] [SHIFT] [STO] [A] (A = ⅓)
Note:-Please use the key [AC] during calculations after you press the key [ON] on any question given
[AC] [(-)] [2] [SHIFT] [STO] [B] (B = -2)
1/α + 1/β
[AC] [1] [ab/c] [ALPHA] [A] [x2] [+] [1] [ab/c] [ALPHA] [B] [=] (2½) press [SHIFT] [d/c] (5/2)
The correct option is “D”
Unforgiveness is a sin, if you don’t forgive; your trespasses (sins) will not be forgiven
Reason. In Mathew 6:14-15- if ye forgive men their trespasses your heavenly father will also forgive your trespasses but if ye forgive not men their trespasses neither will your father forgive your trespasses
Also in Mark 11:25-26- And when ye stand praying forgive if you have ought against any that your father also which is in heaven will forgive your trespasses. But if ye do not forgive, neither will your father which is in heaven forgive your trespasses.
For your heavenly father to forgive your trespasses. You must forgive those that trespass against you including your enemies. In Matthew 5:44-Love your enemies, bless them that curse you, do good to them that hate you, pray for them which despitefully use you and persecute you. As a Christian/Believer of JESUS CHRIST you must forgive your enemies including those that commit evil against you because if you don’t forgive them you are in darkness. In 1 John 2:9-11 – He that saith he is in the light and hateth his brother is in darkness even until now. He that loveth his brother abideth in the light and there is none occasion of stumbling in him. But he that hateth his brother is in darkness and walketh in darkness and knoweth not wither because that darkness has blinded his eyes. A believer will say I am in the light by being a deacon, choir, usher, pastor, evangelist, But know that Christians/believers who is indulge in unforgiveness will not inherit the kingdom of God and they will spend their eternity in hell (the fire that never shall be quenched). Mark 9:43
Know that if you don’t forgive today, your prayers will not be answered. But if you are touched by the word of GOD on unforgiveness and you have make a decision in your heart to forgive whomsoever wronged you, offend you, please make this confession
LORD JESUS, as I come to you, have mercy upon me, as I forgive those that offend me today. Forgive me my trespasses; receive me into your kingdom, IN JESUS NAME AMEN.
NOW: that you have confess this prayer of unforgiveness you are free to confess the next prayer below if you are not
Born-again
if you have not born-again or given your life to Jesus Christ say this prayer “Lord JESUS, as I come to you today, Have mercy upon me, Forgive me all my sins, wash me with your precious blood, save my soul, as I receive you today as my lord and personal savior, write my name in the book of life, IN JESUS NAME AMEN.
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