Aptitude Questions: Quadratic Equations Set 13

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Follow the link To solve Quadratic Equations with the help of Number Line

You have to solve equation I and II ,Give answer
A) If X > Y
B) If X < Y
C) If X ≥ Y
D) If X ≤ Y
E) If X = Y or cannot be established

1. I. 2X² + 11X + 12= 0
   II.5Y² + 27Y + 10 = 0
   
   Answer & Explanation

   Answer – 5)If X=Y or cannot be established
   Explanation :
   (2x+3)(x+4) = 0
   X= -3/2, -4
   (5y+2)(y+5) = 0
   Y = -5, -2/5
   -0.4, -1.5, -4, -5 => yxxy
   
   
   
2. I. 25X² + 25X + 6= 0
   II.5Y² +  20Y + 20 = 0
   
   Answer & Explanation

   Answer – 1)If X>Y
   Explanation :
   (5x+2)(5x+3) = 0
   X = -2/5, -3/5
   (5y+10)(y+2) = 0
   Y = -2, -10/5 = -2, -2
   -2/5, -3/5, -2, -2=> xxyy
   x>y
   
   
   
3. I. 3X² + 7X + 4= 0
   II.3Y² +  10Y + 8 = 0
   
   Answer & Explanation

   Answer – 3)If X≥ Y
   Explanation :
   (x+1)(3x+4) = 0
   X=-1, -4/3
   (3y+4)(y+2) =0
   Y = -4/3, -2
   -1, -4/3, -4/3, -2 => xxyy
   X≥ Y
   
   
   
4. I.(x+y)² = 900
   II.Y + 1689 = 1705
   
   Answer & Explanation

   Answer – 2)If X<Y
   Explanation :
   y = 1705 – 1689 = 16
   (x + y)² = 900
   x + y = 30
   x = 30 – 16 = 14
   16>14
   Clearly, x < y
   
   
   
5. I.8X² + 3X – 38= 0
   II.6Y² –  29Y + 34 = 0
   
   Answer & Explanation

   Answer – 4)If X≤ Y
   Explanation :
   8X² + 3X – 38= 0
   (8x + 19) (x – 2) = 0
   x = 2 or -19/8
   6Y² –  29Y + 34 = 0
   (y – 2) (6y – 17) = 0
   y = 2 or 17/6
   17/6, 2, 2, -19/8 => yyxx
   X≤ Y
   
   
   
6. 9x – 3x = 64.55 + 19.45
   √(y *155) = 7 + 6
   
   Answer & Explanation

   Answer – 5)If X=Y or cannot be established
   Explanation :
   9x – 3x = 64.55 + 19.45
   6x = 84
   x = 14
   √(y *155) = 7 + 6 =13
   y + 155 = 169
   y = 169 – 155 = 14
   x=y
   
   
   
7. I.2X² + 19X + 44= 0
   II.2Y² +  3Y – 20 = 0
   
   Answer & Explanation

   Answer – 4)If X≤ Y
   Explanation :
   2X² + 19X + 44= 0
   (x + 4) (2x + 11) = 0
   x = -4 or -11/2
   2Y² +  3Y – 20 = 0
   (y + 4) (2y – 5) = 0
   y = -4 or 5/2
   5/2, -4,-4,-5/2 = yyxx
   X≤ Y
   
   
   
8. I.P² + 9P = 2P – 12
   II.4Q² +  8Q = 4Q + 8
   
   Answer & Explanation

   Answer – 2)If X<Y
   Explanation :
   p² + 9p = 2p – 12
   (p + 3) (p + 4 ) = 0
   p = – 3, – 4
   4q² + 8q = 4q + 8
   4q2 + 4q – 8 = 0
   (q + 2) (q – 1) = 0
   q = -2, 1
   1, -2,-3,-4 => QQPP
   P<Q
   
   
   
9. I.2X² – 7X + 6= 0
   II.4Y² = 9
   
   Answer & Explanation

   Answer – 3)If X≥ Y
   Explanation :
   2X² – 7X + 6= 0
   (x – 2) (2x – 3) = 0
   x = 2 or x =3/2
   4Y² = 9
   Y = ±3/2 = 3/2, -3/2
   2,3/2,3/2,-3/2 = xxyy
   x≥y
   
   
   
10. I. X²  = 1296
    II.Y  = √1296
    
    Answer & Explanation

    Answer – 4)If X≤ Y
    Explanation :
    X = ±36
    Y = 36
    X≤Y
    
    
    

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