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.

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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.



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