Quadratic Equations with Solution for IBPS PO 2016

In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer

1) if x < y

2) if x > y

3) if x ≤ y

4) if x≥ y

5) if x = y, or relationship between x and y can't be established.

Before going to attempt these question once READ IT

Ques 1.

2x² -15x + 28 = 0  ;   4y² – 23y + 30 = 0

Solution :

==>2x^2 -15x + 28 = 0

==>2x^2 -8x-7x + 28 = 0
==>x = 8/2 , 7/2 = 4, 3.5

==>4y2 – 23y + 30 = 0
==>4y2 – 15y – 8y + 3 = 0
==>y = 15/4 , 8/4 = 3.75, 2

x = y, or relationship between x and y can't be established.

Ques 2.

6x^2-49x+99=0 ; 5y^2+17y+14=0

Solution :

==> 6x^2 - 27x-22x+99 = 0 

==> X = 27/6 ; 22/6

==> X = 9/2 ; 11/3

==> 5y^2+10y+7y+14 = 0

==>Y = -10/5 ; -7/5

==> Y = -2 ; -7/5
x > y

Ques 3.

3x^2 – 20 x + 33 = 0   ; 2y^2 – 11 y + 15 = 0

Solution :

3x^2-11x-9x+33 = 0

==> X = 11/3 ; 9/3 

==> X = 11/3 ; 3

==> 2y^2-6x-5x+15 = 0

==> Y = 6/2 ; 5/2 

==> Y = 3 ; 5/2 
x≥ y

Ques 4.

3x² – 4x – 32 = 0 ; 2y² – 17y + 36 = 0

Solution :

==> 3x^2-12x+8x-32 = 0

==> X = 12/3 ; -8/3

==> X = 4 ; -8/3 

==> 2y^2-9y-8y+36 = 0 

==> Y = 9/2 ; 8/2 

==> Y = 9/2 ; 4 
x ≤ y

Ques 5.

2x^2+ 11x+ 14=0 ; 4y^2+ 12y +9 =0

Solution :

==> 2x^2+7x+4x+14 = 0

==> x = -7/2 ; -4/2

==> x = -7/2 ; -2 

==> 4y^2+6x+6x+9 = 0

==> Y = -6/4 ; -6/4 = 0

==> Y = -3/2 ; -3/2
X < Y

Ques 6.

5x^2–13x – 6 = 0 ; 3y^2+14y+ 8 = 0

Solution :

==> 5x^2-15x-2x-6 = 0

==> X = 15/5 ; -2/5 

==> X = 3 ; -2/5 

==> 3y^2+12y+2y+8 =0

==> Y = -12/3 ; -2/3

==> Y = -4 ; -2/3
X > Y

Ques 7.

3x^2-14x+15=0 ; 2y^2-9y+9=0

Solution  :

==> 3x^2-9x-5x+15 = 0

==> X = 9/3 ; 5/3 

==> X = 3 ; 5/3 

==> 2Y^2-6y-3y+9 = 0

==> Y = 6/2 ; 3/2

==> Y = 3 ; 3/2 
x≥ y

Ques 8.

x^2 – 18x + 72= 0 ; 5y^2 – 18y + 9 = 0

Solution :

==> X^2-12x-6x+72 = 0 

==> X = 12/1 ; 6/1

==> X = 12 ; 6

==> y^2-15y-3y +72 =0 

==> Y = 15/5 ; 3/5

==> Y = 3/5 ; 3 
X>Y

Ques 9.

4X+ 19X + 21= 0 ; 2Y^2– 23Y + 63 = 0

Solution :

==>4x^2+12x+7x+21 =0 

==> X = -12/4 ; -7/4

==> X = -3 ; -7/4 

==> 2y^2-14y-9y+63 =0 

==> Y = 14/2 ; 9/2 

==> Y = 7 ; 9/2 
x < y

Ques 10.

3X^2– 19X + 28= 0 ; 4Y^2 – 29Y + 45 = 0

Solution :
==> 3X^2-12X-7X+28= 0
==> X = 12/3 ; 7/3 
==> X = 4 ; 7/3 

==> 4y^2-20y-9y+45 =0
==> Y = 20/4 ; 9/4
==> Y = 5 ; 9/4 

x = y, or relationship between x and y can't be established.