# Quantitative Aptitude: Quadratic Equations Questions Set 68

1. In each of these questions, two equations (a) and (b) are given. You have to solve both the equations and give answer.
2m2+11m+14=0
4n2+12n+9=0
if m < n
if m > n
if m ≤ n
If m ≥ n
if m = n or no relation can be established
Option A
From eq (a),2m^2+4m+7m+14=0
2m(m+2)+7(m+2)=0
m= -2,-3.5
From eq (b),(2n+3)^2=0
n= -1.5 , -1.5

2. m^2 – 4 = 0
n^2 + 6n + 9=0
if m < n
if m > n
if m ≤ n
If m ≥ n
if m = n or no relation can be established
Option B
From eq(a),m = +-2
From eq(b), n^2 + 3n + 3n + 9=0
n = -3 ,- 3

3. m^2 – 7m + 12 = 0
n^2 + n -12=0
if m < n
if m > n
if m ≤ n
If m ≥ n
if m = n or no relation can be established
Option D
From eq (a), m^2 – 3m – 4m +12=0
m(m-3)-4(m-3)=0
m=3,4
From eq(b) , n(n+4) -3(n+4) = 0
n =3, -4

4. m^2 = 729
n = √529
if m < n
if m > n
if m ≤ n
If m ≥ n
if m = n or no relation can be established
Option E
m = +-27
n = 23

5. m^4 – 227 = 398
n^2 + 321 = 346
if m < n
if m > n
if m ≤ n
If m ≥ n
if m = n or no relation can be established
Option E
m^4 = 625 = +-5
n^2 = 346-321 =+-5

6. x^2 – 12p +35=0
q^2 – 25=0
if x > y
if x ≥ y
if x < y
if x ≤ y
if x = y or there is no relation between ‘x’ and ‘y’
Option B
From eq(a) , x^2 -7x – 5x +35 =0
x(x-7) – 5(x-7)=0
x= 5,7
From eq (b) ,y = 5 , -5

7. 2x^2+5x -12=0
2y^2 -y – 1=0
if x > y
if x ≥ y
if x < y
if x ≤ y
if x = y or there is no relation between ‘x’ and ‘y’
Option E
From eq(a) , 2x^2+8x-3x-12=0
2x(x+4)-3(x+4)=0
x=1.5 , -4
From eq(b) , 2y^2 – 2y +y – 1=0
y = -0.5 , 1

8. x^2=49
y^2+15y+56 =0
if x > y
if x ≥ y
if x < y
if x ≤ y
if x = y or there is no relation between ‘x’ and ‘y’
Option B
x=7 , -7
y^2 + 7q + 8q + 56=0
y = – 7, -8

9. 4x^2 – 4x+15=0
2y^2 +5y – 7=0
if x > y
if x ≥ y
if x < y
if x ≤ y
if x = y or there is no relation between ‘x’ and ‘y’
Option A

10. (x+y)^2 = 3136
y +2513 = 2569
if x > y
if x ≥ y
if x < y
if x ≤ y
if x = q or there is no relation between ‘x’ and ‘y’
Option C