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