Quant Notes | Inequalities

This topic we learn in our school days using basic method, but here we learn for competitive exams thats for accuracy and time are main factor .Now we will learn some basic and shortcut trick to solve quadratic equation.

 An equation in which the highest power of the variable is 2 is called a quadratic equation. 

example, ax²+bx+c=0 denotes a quadratic equation.

a, b and c are known values. a can't be 0.  "x" is the variable or unknown

When we solved a quadratic equation, it will always gives two values of variable. these values are called roots of the equation or expression.

   1.  By taking square roots or Factor Method

   2.  By Quadratic Formula

 

Factor Method

 

eg. x² + 3x − 4

 

 

It is worth remembering these, as they can make factoring easier.

formula

 

   2.  By Quadratic Formula

 

 

 

1. x² – 34x + 288 = 0
   y² – 28y + 192 = 0
A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
E. X = Y or relation cannot be established

2. x² – 26x + 168 = 0
    y² – 32y + 252 = 0
A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
E. X = Y or relation cannot be established

3. x² + 26x + 168 = 0
    y² + 23y + 132 = 0
A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
E. X = Y or relation cannot be established

4. x² – 28x + 195 = 0
    y² – 30y + 216 = 0
A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
E. X = Y or relation cannot be established

5. (x – 19)² = 0
     y² = 361
A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
E. X = Y or relation cannot be established

6. x² = 121
    y² – 46y + 529 = 0
A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
E. X = Y or relation cannot be established