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# 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.

#### Ramandeep Singh - Educator

I'm Ramandeep Singh, your guide to banking and insurance exams. With 14 years of experience and over 5000 successful selections, I understand the path to success firsthand, having transitioned from Dena Bank and SBI. I'm passionate about helping you achieve your banking and insurance dreams.