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How to Construct a Quadratic Equation when the roots are given

Construct a quadratic equation whose root are - ½ and 2
(1). (A)3x^2 – 3x + 2 = 0 (B)3x^2 + 3x – 2 = 0 (C)2x^2 + 3x – 2 = 0 (D)2x^2 – 3x - 2 = 0
Solution:- Using CASIO fx-991MS calculator, make x = - 1/ 2 and x = 2, To produce the correct answer first make x = - ½
Checking option(A)3x^2 – 3x + 2 = 0
[ON] [(-)] [1] [a b /c ] [2] [SHIFT] [STO] [X] (x = -1 /2 )
Note:-Please use the key [AC] during calculations after you press the key [ON] on any question given
[AC] [3] [ALPHA] [X] [x2 ] [-] [3] [ALPHA] [X] [+] [2] [=] (4.75)
Option (A) is wrong because it did not give zero. Since it did not give zero don't bother to calculate the other root go to the next option
Checking option (B)3x^2 + 3x – 2 = 0
make one of the factors x = - ½
[AC] [(-)] [1] [a b /c] [2] [SHIFT] [STO] [X] (x = - ½)
[AC] [3] [ALPHA] [X] [x2 ] [+] [3] [ALPHA] [X] [-] [2] [=] (-2.75)
Option (B) is wrong because it did not give zero. Since it did not give zero don't bother to calculate the other root go to the next option
Checking option (C)2x^2 + 3x – 2 = 0
make one of the factors x = - ½
[AC] [(-)] [1] [a b /c] [2] [SHIFT] [STO] [X] (x = - ½)
[AC] [2] [ALPHA] [X] [x2 ] [+] [3] [ALPHA] [X] [-] [2] [=] (-3)
Option (C) is wrong because it did not give zero. Since it did not give zero don't bother to calculate the other root go to the next option
Checking option (D)2x^2 – 3x + 2 = 0
make one of the factors x= - ½
[AC] [(-)] [1] [a b /c] [2] [SHIFT] [STO] [X] (x = - ½)
[AC] [2] [ALPHA] [X] [x2 ] [-] [3] [ALPHA] [X] [+] [2] [=] (0)
one of the root is correct because it gives zero. Since it gives zero calculate the other root go to the next factor x = 2 make the other root x=2
[AC] [2] [STO] [X] (x=2)
[AC] [2] [ALPHA] [X] [X2 ] [-] [3] [ALPHA] [X] [-] [2] [=](0)
if the roots -1/2 and 2 is equal to 2x2 -3x+2 option E is correct The correct option is option “(D)” because it is equal to zero
OR
(2). Construct a quadratic equation whose root are - ½ and 2
(A)3x^2 – 3x + 2 = 0 (B)3x^2 + 3x – 2 = 0 (C)2x^2 + 3x – 2 = 0 (D)2x^2 – 3x + 2 = 0
Solution:- Using CASIO fx-991MS calculator
Checking option (A) 3x 2 – 3x + 2 = 0
Solving the equation  3x^2 – 3x + 2 = 0 ------ax^2 + bx + c = 0 where a = 3, b = -3, c = 2
Press [ON] [MODE] [MODE] [MODE] [1] [→] [2] [3] [=] [(-)] [3] [=] [2] [=] (X 1 = 0.5) press [a b /c] ( ½ ) press [=] or [↓] (X 2 = 0.5) press [MODE] [1]
Option “A” is wrong because  it didn’t give the roots as    - ½ and 2. Go to the next option
Checking option (B) 3x2 + 3x – 2 = 0
Solving the equation  3x^2 + 3x – 2 = 0 ------ax^2 + bx + c = 0 where a = 3, b = 3, c = -2
Press [ON] [MODE] [MODE] [MODE] [1] [→] [2] [3] [=] [3] [=] [(-)] [2] [=] (X 1 = 0.457427107) press [=] or [↓] (X 2 = 0.5) press [MODE] [1]
Option “B” is wrong because  it didn’t give the roots as    - ½ and 2. Go to the next option
Checking option (C) 2x^2 + 3x – 2 = 0
Solving the equation  3x^2 + 3x – 2 = 0 ------ax^2 + bx + c = 0 where a = 3, b = 3, c = -2
Press [ON] [MODE] [MODE] [MODE] [1] [→] [2] [2] [=] [3] [=] [(-)] [2] [=] (X 1 = 0.5) press [a b /c] (½) [=] or [↓] (X 2 = -2) press [MODE] [1]
Option “C” is correct because  it  give the roots as    - ½ and 2. The correct option is “c”

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