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Quadratic Equations Shortcut trick for SBI PO | Questions with Solutions

Quadratic Equations Shortcut trick for SBI PO | Questions with Solutions

In the following questions, two equations numbered I and II are given. You have to solve both the equations and

Give answer (1) if x>y
Give answer (2) if x ≥ y
Give answer (3) if x < y
Give answer (4) if x ≤y
Give answer (5) if x=y (Or) the relationship cannot be established.

1.)   I. 40x2 – 47x +12 =0.

        II. 5y2 – 51y + 54 =0.

Normal Method: (Factorization Method)

I. 40x2 – 47x +12 =0

40x2 – 32x-15x +12 =0

8x(5x– 4) – 3(5x -4) =0
(8x-3) (5x-4)=0
8x-3 =0, 5x-4 =0
X= 3/8,  4/5.

II. 5y2 – 51y + 54 =0.
5y2 – 45y -6y + 54 =0.
5y (y-9) -6(y-9)=0,
(5y-6 ) (y-9) =0
6/5, 9
Clearly, x < y  Answer (1) 

Shortcut Trick to solve :40x2 – 47x +12 =0

1) split the middle term so as to get,
the sum of the two numbers is -47 and
Product of two numbers should be (12 *40) = 480

 

2)      I. 22x2 – x -6 =0.

          II. 63y2 – 11y -40 =0.

Factorization Method:

I. 22x2 – x -6 =0.

  • 22x2 – 12x + 11x -6 =0.
  • 11x( 2x+1) – 6(2x+1) =0
  • (11x-6)(2x+1)=0

X=6/11, -1/2.

II. 63y2 – 11y -40 =0.

  • 63y2 – 56y + 45y – 40 =0.
  • 7y (9y-8) + 5(9y -8) =0,
  • (7y+5) (9y-8) =0,

y = -5/7,  8/9.

Answer: (5).

3.   I. 20x2 – 37x + 8 =0.

      II. 24y2 +38y -7 =0.

    I. 20x2 – 37x + 8 =0.

  • 20x2 – 32x -5x + 8 =0.
  • 4x(5x-8)-1(5x-8)=0,
  • (4x-1)(5x-8)=0,

= ¼, 8/5.

II. 24y2 +38y -7 =0.

  • 24y2 +42y-4y -7 =0.
  • 6y (4y +7)-1(4y+7)=0
  • (4y+7)(6y-1)=0

= -7/4 or 1/6.

Clearly, x>y  Answer (1).

4.    I. 12x2 – 28x +15 =0.

        II. 4y2 – 20y + 21 =0.

12x2 – 28x +15 =0.

  • 12x2 – 10x -18x +15 =0.
  • 2x (6x – 5) -3(6x -5) =0.
  • (2x-3) (6x-5) =0

= 2/3, 5/6.

4y2 – 20y + 21 =0.

  • 4y2 – 14y-6y + 21 =0.
  • 2y( 2y-7) – 3(2y-7) =0

= 3/2, 7/2.

Clearly, x ≤y. Answer (4).

5.   I. 14x2 – 89x +30 =0.

      II. 27y2 – 12y + 1 =0.

Clearly x > y. Answer (1).






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