Quantitative Aptitude: Quadratic Equations Questions Set 64

1. x³ – 4x² + 3x = 0
   7y³ – 23y² + 6y = 0
   
   x
   x<=y
   x>y
   x>=y
   none
   Option D
   x³ – 4x² + 3x = 0
   This gives x(x² – 4x + 3) = 0
   ⇒ x(x - 3)(x - 1) = 0
   ⇒ x = 0, 1 or 3
   7y³ – 23y² + 6y = 0
   ⇒y(7y² – 23y + 6) = 0
   ⇒y(7y - 2)(y - 3) = 0
   ⇒ y = 0, 2/7 or 3
   x>=y
   
   
    



2. x²+34x+289=0
   y²+28y+196=0
   
   x
   x<=y
   x>y
   x>=y
   none
   Option A
   
   x²+17x+17x+289=0
   So, X =-17
   
   Y = -14
   =>x
   
   
    



3. 4X² + 24X + 36 =0
   5Y² + 20Y + 20 =0
   
   x
   x<=y
   x>y
   x>=y
   none
   Option A
   4X² + 24X + 36 =0
   X² + 6X + 9 =0
   X² + 3X + 3x + 9 =0
   X = -3
   5Y² + 20Y + 20 =0
   Y² + 4Y + 4 =0
   Y² + 4Y + 4y + 4 =0
   Y= -2
   So, Y>X
   
   
    



4. x⁵ = 32
   y¹⁰ = 1024
   
   x
   x<=y
   x>y
   x>=y
   none
   Option D
   x = 2 and y = + /- 2
   
    



5. x² + x = 56
   y² - 17y + 72 = 0
   
   x
   x<=y
   x>y
   x>=y
   none
   Option A
   x² + x = 56
   x² + 8x - 7x -56 = 0
   x(x+8) -7 (x+8) =0
   (x+8) (x-7) =0
   x= -8 , 7
   y² - 17y + 72 = 0
   y² - 9y - 8y + 72 =0
   y(y-9) -8(y-9) = 0
   (y-9) (y-8) =0
   y= 9, 8
   x < y
   
   
    



6. 3x² +13x +14 = 0
   3y²+11y+10 = 0
   
   x
   x<=y
   x>y
   x>=y
   none
   Option B
   . 3x² +13x +14 = 0
   => (3x+7) (x+2)
   => x = -7/3, -2
   3y²+11y+10 = 0
   => (y+2) (3y+5)
   => y = -2 , -5/3
   So x ≤ y
   
   
   
    



7. 144x² – 23 = 2
   12y+√25=√100
   
   x
   x<=y
   x>y
   x>=y
   none
   Option B
   144x² = 23+2=25
   x²=25/144
   =>x=+or- 5/12
   12y+√25=√100
   12y= = 5
   y=5/12
   y ≥ x
   
   
   
    



8. x² – 32x + 255 = 0
   y² - 39y + 378= 0
   
   x
   x<=y
   x>y
   x>=y
   none
   Option A
   x² – 32x + 255 = 0
   x² - 15x – 17x + 255 = 0
   x(x-15)-17(x-15)=0
   (x-15)(x-17)=0
   x=15,17
   y² - 39y + 378 = 0
   y² - 18y – 21y + 378 = 0
   y(y-18)-21(y-18)=0
   (y-18)(y-21)=0
   y=18, 21
   y>x
   
   
    



9. x² – 15x + 84 = 4x
   y² – 15y + 156 = 10y
   
   x
   x<=y
   x>y
   x>=y
   none
   Option B
   x² – 15x + 84 = 4x
   ⇒ x² – 19x + 84 = 0
   ⇒ x² – 12x – 7x + 84 = 0
   ⇒ x( x – 12) – 7 ( x – 12) = 0
   ⇒ (x – 7) (x – 12) = 0
   ⇒ x = 7, 12
   
   y² – 15y + 156 = 10y
   ⇒ y² -25y + 156 = 0
   ⇒ y² – 12y – 13y + 156 = 0
   ⇒ y( y – 12) – 13 ( y – 12) = 0
   ⇒ (y – 13) (y – 12) = 0
   ⇒ y = 13, 12
   ∴ y ≥ x
   
   
    



10. 6x + 3y = 24
    x +2y = 8.5
    
    x
    x<=y
    x>y
    x>=y
    none
    Option A
    x = 2.5 y = 3 heyce, x < y